Question 14 Marks
Solve the following quadratic equation using formula method only
$x^2-4 \sqrt{15} x-4=0$
Answer$x ^2-4 \sqrt{15} x -4=0$
$a =1 ; b =-4 \sqrt{15} ; c=-4 $
$ D = b ^2-4 ac $
$ =(-4 \sqrt{15})^2-4(1)(-4)$
$ =240+16 $
$=256 $
$ x =\frac{- b \pm \sqrt{ b ^2-4 ac }}{2 a} $
$ x =\frac{4 \sqrt{15} \pm \sqrt{256}}{2} $
$ x =\frac{4 \sqrt{15}+16}{2}, x =\frac{4 \sqrt{15}-16}{2} $
$x =2 \sqrt{15}+8, x=2 \sqrt{15}-8$
View full question & answer→Question 24 Marks
Solve the following quadratic equation using formula method only
$x ^2+\frac{1}{2} x -1=0$
Answer$x ^2+\frac{1}{2} x -1=0 $
$ 2 x ^2+ x -2=0$
$ a =2 ; b =1 ; c=-2 $
$D = b ^2-4 ac$
$=(1)^2-4(2)(-2) $
$=1+16$
$ =17 $
$ x =\frac{- b \pm \sqrt{ b ^2-4 ac }}{2 a} $
$ x =\frac{-1 \pm \sqrt{17}}{4} $
$x =\frac{-1+\sqrt{17}}{4}, x=\frac{-1-\sqrt{17}}{4}$
View full question & answer→Question 34 Marks
Solve the following quadratic equation using formula method only
$\sqrt{3} x^2+10 x-8 \sqrt{3}=0$
Answer$\sqrt{3} x^2+10 x-8 \sqrt{3}=0$
$a=\sqrt{3} ; b=10 ; c=-\frac{8}{\sqrt{3}}$
$ D=b^2-4 a c$
$ =(10)^2-4(\sqrt{3})(-8 \sqrt{3})$
$=100+96 $
$=196$
$x =\frac{- b \pm \sqrt{ b ^2-4 ac }}{2 a}$
$ x=\frac{-10 \pm \sqrt{196}}{2 \sqrt{3}} $
$ x=\frac{-10+14}{2 \sqrt{3}}, x=\frac{-10-14}{2 \sqrt{3}} $
$x=\frac{4}{2 \sqrt{3}}, x=\frac{24}{2 \sqrt{3}} $
$x=\frac{2}{\sqrt{3}}, x=-\frac{12}{\sqrt{3}}$
View full question & answer→Question 44 Marks
Solve the following quadratic equation using formula method only
$x^2+\frac{1}{2} x=3$
Answer$x ^2+\frac{1}{2} x =3 $
$ 2 x ^2+ x =6$
$ 2 x ^2+ x -6=0 $
$ a =2 ; b =1 ; c=-6$
$ D=b^2-4 ac$
$=(1)^2-4(2)(-6)$
$ =1+48$
$ =49$
$x =\frac{- b \pm \sqrt{ b ^2-4 ac }}{2 a} $
$ x =\frac{-1 \pm \sqrt{49}}{4} $
$ x =\frac{-1+7}{4}, x=\frac{-1-7}{4} $
$ x=\frac{6}{4}, x=-\frac{8}{4} $
$ x=\frac{3}{2}, x=-2$
View full question & answer→Question 54 Marks
Solve the following quadratic equation using formula method only
$3x^2 + 12 = 32 x$
Answer$3 x^2+12=32 x $
$ 3 x^2-32 x+12=0 $
$ a=3 ; b=-32 ; c=12$
$ D=b^2-4 a c $
$ =(-32)^2-4(3)(12) $
$ =1024-144 $
$=880$
$x=\frac{-b \pm \sqrt{b^2-4 ac }}{2 a} $
$x=\frac{32 \pm \sqrt{880}}{6}$
$ x=\frac{32+4 \sqrt{55}}{6}, x=\frac{32-4 \sqrt{55}}{6}$
$ x=\frac{16+2 \sqrt{55}}{3}, x=\frac{16-2 \sqrt{55}}{3}$
View full question & answer→Question 64 Marks
Solve the following quadratic equation using formula method only
$3 x ^2+2 \sqrt{5} x -5=0$
Answer$3 x^2+2 \sqrt{5} x-5=0 $
$ a=3 ; b=2 \sqrt{5} ; c=-5$
$ D=b^2-4 a c $
$=(2 \sqrt{5})^2-4(3)(-5) $
$ =20+60$
$ =80$
$x=\frac{-b \pm \sqrt{b^2-4 ac }}{2 a}$
$ x=\frac{-(2 \sqrt{5}) \pm \sqrt{80}}{6} $
$ x=\frac{-(2 \sqrt{5}) \pm 4 \sqrt{5}}{6} $
$x=\frac{-(2 \sqrt{5}) \pm 4 \sqrt{5}}{6} $
$ x=\frac{-2 \sqrt{5}+4 \sqrt{5}}{6}, x=\frac{-2 \sqrt{5}-4 \sqrt{5}}{6} $
$x=\frac{\sqrt{5}}{3}, x=-\sqrt{5}$
View full question & answer→Question 74 Marks
Solve the following quadratic equation using formula method only
$16x^2 - 24x = 1$
Answer$16 x ^2-24 x =1 $
$ 16 x ^2-24 x -1=0 $
$ a =16 ; b =-24 ; c=-1$
$ D = b ^2-4 ac $
$=(-24)^2-4(16)(-1) $
$ =576+64$
$=640$
$ x =\frac{- b \pm \sqrt{ b ^2-4 ac }}{2 a}$
$ x =\frac{24 \pm 8 \sqrt{10}}{32} $
$ x =\frac{3+\sqrt{10}}{4}, x=\frac{3-\sqrt{10}}{4}$
View full question & answer→Question 84 Marks
Solve the following quadratic equation using formula method only
$25x^2 + 30x + 7 = 0$
Answer$25 x^2+30 x+7=0 $
$a=25 ; b=30 ; c=7$
$ D=b^2-4 a c$
$ =(30)^2-4(25)(7) $
$ =900-700 $
$ =200$
$ x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} $
$x=\frac{-30 \pm \sqrt{200}}{50} $
$ x=\frac{-30+10 \sqrt{2}}{50} \times=\frac{-30-10 \sqrt{2}}{50}$
$ x=\frac{-3+\sqrt{2}}{5}, x=\frac{-3-\sqrt{2}}{5}$
View full question & answer→Question 94 Marks
Solve the following quadratic equation using formula method only
$4 - 11 x = 3x^2$
Answer$4-11 x=3 x^2 $
$ 3 x^2+11 x-4=0 $
$a=3 ; b=11 ; c=-4$
$ D=b^2-4 a c $
$ =(11)^2-4(3)(-4) $
$=121+48$
$=169$
$x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} $
$x=\frac{-11 \pm \sqrt{169}}{6} $
$x=\frac{-11+13}{6}, x=\frac{-11-13}{6} $
$ x=\frac{2}{6}, x=-\frac{24}{6} $
$x=\frac{1}{3}, x=-4$
View full question & answer→Question 104 Marks
Solve the following quadratic equation using formula method only
$15x^2 - 28 = x$
Answer$15 x^2-28=x $
$ 15 x^2-x-28=x$
$ a=15 ; b=-1 ; c=-28$
$D=b^2-4 a c $
$=(-1)^2-4(15)(-28) $
$=1+1680$
$ =1681$
$x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} $
$ x=\frac{1 \pm \sqrt{1681}}{30} $
$x=\frac{1+41}{30}, x=\frac{1-41}{30} $
$ x=\frac{42}{30}, x=-\frac{40}{30} $
$x=\frac{7}{5} \quad, x=-\frac{4}{3}$
View full question & answer→Question 114 Marks
Solve the following quadratic equation using formula method only
$\frac{5}{4} x^2-2 \sqrt{5} x+4=0$
Answer$\frac{5}{4} x^2-2 \sqrt{5} x+4=0$
$ 5 x^2-8 \sqrt{5} x+16=0$
$ a=5 ; b=-8 \sqrt{5} ; c=16$
$D=b^2-4 a c$
$ =(-8 \sqrt{5})^2-4(5)(15)$
$ =40-300 \\ =-260$
$x=\frac{-b \pm \sqrt{b^2-4 ac }}{2 a} $
$ x=\frac{-(-8 \sqrt{5}) \pm \sqrt{-260}}{2 \times 5} $
$ x=\frac{8 \sqrt{5} \pm \sqrt{-260}}{2 \times 5}$
$ x=\frac{4 \sqrt{5}}{5} \quad \text { (Since } \sqrt{-260} \text { is not possible) }$
View full question & answer→Question 124 Marks
Solve the following quadratic equation using formula method only :
$2 x+5 \sqrt{3} x+6=0$
Answer$2 x+5 \sqrt{3} x+6=0 $
$ a =2 ; b =5 \sqrt{3} ; c =6 $
$ D = b ^2-4 ac $
$ D =(5 \sqrt{3})^2-4(2)(6) $
$ =75-48 $
$ =27$
$x=\frac{-b \pm \sqrt{b^2-4 ac }}{2 a}$
$ x=\frac{-(5 \sqrt{3}) \pm 3 \sqrt{3}}{4}$
$ x=\frac{-(5 \sqrt{3})+3 \sqrt{3}}{4}, x=\frac{-(5 \sqrt{3})-3 \sqrt{3}}{4}$
$ x=\frac{-2 \sqrt{3}}{4}, x=\frac{-8 \sqrt{3}}{4} $
$ x=-\frac{\sqrt{3}}{2}, x=-2 \sqrt{3}$
View full question & answer→Question 134 Marks
Solve the following quadratic equation using formula method only
$3 x ^2+2 \sqrt{5} x-5=0$
Answer$3 x ^2+2 \sqrt{5} x-5=0$
$ a=3 ; b=2 \sqrt{5} ; c=-5$
$ D=b^2-4 a c $
$=(2 \sqrt{5})^2-4(3)(-5)$
$ =20+60 $
$ =80$
$x =\frac{- b \pm \sqrt{ b ^2-4 ac }}{2 a} $
$ X=\frac{-(2 \sqrt{5}) \pm \sqrt{80}}{6} $
$ x=\frac{-(2 \sqrt{5}) \pm 4 \sqrt{5}}{6} $
$ X=\frac{-(2 \sqrt{5})+4 \sqrt{5}}{6}, X=\frac{-(2 \sqrt{5})-4 \sqrt{5}}{6}$
$ X=\frac{\sqrt{5}}{3}, X=-\sqrt{5}$
View full question & answer→Question 144 Marks
Solve the following quadratic equation using formula method only :
$16x^2 = 24x + 1$
Answer$16 x^2=24 x+1 $
$ 16 x^2-24 x-1=0 $
$ x^2-\frac{3}{2} x-\frac{1}{16}=0$
$ a=1 ; b=-\frac{3}{2} ; c=-\frac{1}{16} $
$ D=b^2-4 a c$
$=\left(-\frac{3}{2}\right)^2-4(1)\left(-\frac{1}{16}\right) $
$ =\frac{9}{4}+\frac{1}{4} \\ =\frac{10}{4}$
$x =\frac{- b \pm \sqrt{ b ^2-4 ac }}{2 a}$
$x =\frac{-\left(-\frac{3}{2}\right) \pm \sqrt{\frac{10}{4}}}{2 \times 1}$
$ x =\frac{3+\sqrt{10}}{4}, x=\frac{3-\sqrt{10}}{4}$
View full question & answer→Question 154 Marks
Solve the following equation:
$\frac{x-1}{2 x+1}+\frac{2 x+1}{x-1}=\frac{5}{2}, x \neq-\frac{1}{2}$
Answer$\frac{x-1}{2 x+1}+\frac{2 x+1}{x-1}=\frac{5}{2} $
$ \frac{( x -1)^2+(2 x +1)^2}{(2 x +1)( x -1)}=\frac{5}{2} $
$ \frac{\left( x ^2-2 x +2\right)+\left(4 x ^2+4 x +1\right)}{2 x ^2- x -1}=\frac{5}{2} $
$ \frac{5 x ^2+2 x +2}{2 x^2- x -1}=\frac{5}{2} $
$ 10 x ^2+4 x +4=10 x ^2-5 x -5 $
$ -9 x -9=0 $
$x +1=0$
$x =-1$
View full question & answer→Question 164 Marks
Solve the following equation:
$\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{5}{6}, x \neq-1,1$
Answer$\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{5}{6}, x \neq-1,1 $
$ \frac{( x +1)^2-( x -1)^2}{( x -1)( x +1)}=\frac{5}{6} $
$ \frac{ x ^2+2 x +1-\left( x ^2-2 x +1\right)}{ x ^2- x + x -1}=\frac{5}{6} $
$ \frac{ x ^2+2 x +1- x ^2+2 x -1}{ x ^2-1}=\frac{5}{6} $
$ 6(4 x)=5\left(x^2-1\right) $
$24 x=5 x^2-5$
$ x ^2-\frac{24}{5} x -1=0$
$ x ^2+\frac{1}{5} x -5 x -1=0 $
$ x\left(x+\frac{1}{5}\right)-5\left(x+\frac{1}{5}\right)=0$
$\left(x+\frac{1}{5}\right)(x-5)=0 $
$x=5, x=-\frac{1}{5} $
View full question & answer→Question 174 Marks
Solve the following equation: $\frac{1}{ x -1}+\frac{2}{ x -1}=\frac{6}{ x },(x \neq 0)$
Answer$\frac{1}{x-1}+\frac{2}{x-1}=\frac{6}{x},(x \neq 0) $
$ \frac{(x-1)+2(x-2)}{(x-2)(x-1)}=\frac{6}{x} $
$ x(x+1)+2 x(x-2)=6(x-2)(x-1) $
$ x^2-x+2 x^2-4 x=6\left(x^2-2 x-x+2\right)$
$ 3 x^2-5 x=6 x^2-18 x+12 $
$3 x^2-13 x+12=0 $
$ x^2-\frac{13}{3} x+4=0 $
$ x^2-3 x-\frac{4}{3} x+4=0$
$ x(x-3)-\frac{4}{3}(x-3)=0$
$ (x-3)\left(x-\frac{4}{3}\right)=0$
$ x=3, x=\frac{4}{3}$
View full question & answer→Question 184 Marks
Solve the following equation: $\frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}$
Answer$\frac{ x +3}{ x -2}-\frac{1- x }{ x }=\frac{17}{4} $
$ \frac{4 x+12}{x-2}-\frac{4-4 x}{x}=17 $
$ x(4 x+12)-(4-4 x)(x-2)=17 x(x-2) $
$ 4 x^2+12 x-\left(4 x-4 x^2-8+8 x\right)=17 x^2-34 x$
$ 4 x^2+12 x-4 x+4 x^2+8-8 x=17 x^2-34 x $
$ 8 x^2+8=17 x^2-34 x $
$ 9 x^2-34 x-8=0$
$ x ^2-\frac{34}{9} x -\frac{8}{9}=0 $
$ x ^2-4 x +\frac{2}{9} x -\frac{8}{9}=0 $
$ x ( x -4)+\frac{2}{9}( x -4)=0 $
$ (x-4)\left(x+\frac{2}{9}\right)=0$
$ x=4, x=-\frac{2}{9} $
View full question & answer→Question 194 Marks
Solve the following equation: $\frac{2 x }{ x -4}+\frac{2 x -5}{ x -3}=\frac{25}{3}$
Answer$\frac{2 x}{x-4}+\frac{2 x-5}{x-3}=\frac{25}{3} $
$ \frac{6 x}{x-4}+\frac{6 x-15}{x-3}=25 $
$ 6 x(x-3)+(6 x-15)(x-4)=25(x-4)(x-3) $
$ 6 x^2-18 x+6 x^2-15 x-24 x+60=25\left(x^2-4 x-3 x+12\right) $
$ 12 x^2-57 x+60=25 x^2-175 x+300 $
$ 13 x^2-118 x+240=0$
$ x^2-\frac{118}{13} x+\frac{240}{13}=0 $
$x^2-6 x-\frac{40}{13} x+\frac{240}{13}=0$
$ x(x-6)-\frac{40}{13}(x-6)=0 $
$ (x+6)\left(x-\frac{40}{13}\right)=0 $
$ x=6, x=\frac{40}{13}$
View full question & answer→Question 204 Marks
Solve the following equation: $\frac{x+3}{x+2}=\frac{3 x-7}{2 x-3}$
Answer$\frac{x+3}{x+2}=\frac{3 x-7}{2 x-3} $
$ (x+3)(2 x-3)=(3 x-7)(x+2)$
$ 2 x^2+6 x-3 x-9=3 x^2-7 x+6 x-14 $
$ 2 x^2+3 x-9=3 x^2-x-14 $
$(3-2) x^2+(-1-3) x+(-14+9)=0 $
$x^2-4 x-5=0 $
$ x^2+x-5 x-5=0 $
$ x(x+1)-5(x+1)=0$
$ (x+1)(x-5)=0 $
$(x+1)=0,(x-5)=0$
$ x=-1, x=5$
View full question & answer→Question 214 Marks
Solve the following: $\left(x-\frac{1}{2}\right)^2=4$
Answer$\left( x -\frac{1}{2}\right)^2=4$
$x^2-x+\frac{1}{4}=4$
$x^2-x-\frac{15}{4}=0$
$x^2+\frac{3}{2} x-\frac{5}{2} x-\frac{15}{4}=0$
$ x \left( x +\frac{3}{2}\right)-\frac{5}{2}\left( x +\frac{3}{2}\right)=0 $
$ \left( x +\frac{3}{2}\right)\left( x -\frac{5}{2}\right)=0$
$x =-\frac{3}{2}, x =\frac{5}{2}$
View full question & answer→Question 224 Marks
Solve the following equation: $4x^2 + 4 bx - (a^2 - b^2) = 0$
Answer$4 x^2+4 b x-\left(a^2-b^2\right)=0 $
$ x^2+b x-\frac{\left(a^2-b^2\right)}{4}=0$
$x ^2+\frac{ a + b }{2} \times-\frac{ a - b }{2} \times-\frac{ a ^2- b ^2}{4}=0$
$x \left\{ x +\frac{ a + b }{2}\right\}-\frac{( a - b )}{2}\left\{ x +\frac{ a + b }{2}\right\}=0$
$\left\{ x +\frac{( a + b )}{2}\right\}\left\{ x -\frac{( a - b )}{2}\right\}=0$
$\left\{ x +\frac{( a + b )}{2}\right\}=0,\left\{ x -\frac{( a - b )}{2}\right\}=0$
$x =-\frac{( a + b )}{2}, x =\frac{( a - b )}{2}$
View full question & answer→Question 234 Marks
Solve the following equation: $a^2x^2 - 3abx + 2b^2 = 0$
Answer$a^2 x^2-3 a b x+2 b^2=0$
$ x^2-3 \frac{b}{a} x+2\left(\frac{b}{a}\right)^2=0 $
$x^2-\frac{b}{a} x-2 \frac{b}{a} x+2\left(\frac{b}{a}\right)^2=0$
$x\left(x-\frac{b}{a}\right)-2 \frac{b}{a}\left(x-\frac{b}{a}\right)=0$
$\left(x-\frac{b}{a}\right)\left(x-2 \frac{b}{a}\right)=0 $
$ \left(x-\frac{b}{a}\right)=0,\left(x-2 \frac{b}{a}\right)=0 $
$x=\frac{b}{a}, x=2 \frac{b}{a}$
View full question & answer→Question 244 Marks
Solve the following equation:
$\sqrt{2} x ^2-3 x -2 \sqrt{2}=0$
Answer$\sqrt{2} x^2-3 x-2 \sqrt{2}=0 $
$ x^2-\frac{3}{\sqrt{2}} x-2=0 $
$x^2+\frac{1}{\sqrt{2}} x-2 \sqrt{2}-2=0$
$ x\left(x+\frac{1}{\sqrt{2}}\right)-2 \sqrt{2}\left(x+\frac{1}{\sqrt{2}}\right)=0$
$\left(x+\frac{1}{\sqrt{2}}\right)(x-2 \sqrt{2})=0 $
$\left(x+\frac{1}{\sqrt{2}}\right)=0,(x-2 \sqrt{2})=0$
$x=-\frac{1}{\sqrt{2}}, x=2 \sqrt{2}$
View full question & answer→Question 254 Marks
Solve the following equation: c
Answer$\frac{2}{x^2}-\frac{5}{x}+2=0$
$ 2-5 x+2 x^2=0$
$ 2 x^2-5 x+2=0$
$x^2-\frac{5}{2} x +1=0 $
$ x ^2-2 x-\frac{1}{2} x +1=0 $
$x ( x -2)-\frac{1}{2}( x -2)=0$
$ ( x -2)\left( x -\frac{1}{2}\right)=0 $
$ ( x -2)=0,\left( x -\frac{1}{2}\right)=0 $
$ x =2, x =\frac{1}{2}$
View full question & answer→Question 264 Marks
Solve the following equation: $10 x -\frac{1}{ x }=3$
Answer$10 x -\frac{1}{ x }=3$
$ 10 x ^2-1=3 x $
$10 x ^2-3 x -1=0 $
$ x ^2-\frac{3}{10} x -\frac{1}{10}=0$
$ x ^2+\frac{1}{5} x -\frac{1}{2} x -\frac{1}{10}=0$
$ x \left( x +\frac{1}{5}\right)-\frac{1}{2}\left( x +\frac{1}{5}\right)=0$
$\left( x +\frac{1}{5}\right)\left( x -\frac{1}{2}\right)=0 $
$ \left( x +\frac{1}{5}\right)=0,\left( x -\frac{1}{2}\right)=0 $
$ x =-\frac{1}{5}, x=\frac{1}{2}$
View full question & answer→Question 274 Marks
Solve the following quadratic equation using formula method only $3a^2x^2 +8abx + 4b^2 = 0, a \neq 0$
Answer$3 a^2 x^2+8 a b x+4 b^2=0$
$x ^2+\frac{8 b }{3 a } x +\frac{4 b ^2}{3 a ^2}=0$
$a=1 ; b=\frac{8 b}{3 a} ; c=\frac{4 b^2}{3 a^2}$
$D=b^2-4 a c$
$=\left(\frac{8 b }{3 a }\right)^2-4(1)\left(\frac{4 b ^2}{3 a ^2}\right)$
$=\frac{64 b^2}{9 a^2}-\frac{16 b^2}{3 a^2}$
$=\frac{64 b^2-48 b^2}{9 a^2}=\frac{16 b^2}{9 a^2}$
$x =\frac{- b \pm \sqrt{ b ^2-4 ac }}{2 a}$
$x=\frac{-\frac{8 b }{3 a } \pm \sqrt{\frac{16 b ^2}{9 a ^2}}}{2}$
$x=\frac{-\frac{8 b}{3 a}+\frac{4 b}{3 a}}{2}, x=\frac{-\frac{8 b}{3 a}-\frac{4 b}{3 a}}{2}$
$x=\frac{-4 b}{6 a}, x=\frac{-12 b}{6 a}$
$x=-\frac{2 b}{3 a}, x=-\frac{2 b}{a}$
View full question & answer→Question 284 Marks
Solve the following equation : $\frac{ x -1}{ x -2}+\frac{ x -3}{ x -4}=3 \frac{1}{3}$
Answer$\frac{ x -1}{ x -2}+\frac{ x -3}{ x -4}=3 \frac{1}{3}$
$\frac{( x -1)( x -4)+( x -3)( x -2)}{( x -2)( x -4)}=\frac{10}{3}$
$\frac{x^2-5 x+4+x^2-5 x+6}{x^2-6 x+8}=\frac{10}{3}$
$\frac{2 x^2-10 x+10}{x^2-6 x+8}=\frac{10}{3}$
$6 x^2-30 x+30=10 x^2-60 x+80$
$4 x^2-30 x+50=0$
$2 x^2-15 x+25=0$
$x ^2-\frac{15}{2} x +\frac{25}{2}=0$
$x^2-5 x-\frac{5}{2} x+\frac{25}{2}=0$
$x(x-5)-\frac{5}{2}(x-5)=0$
$(x-5)\left(x-\frac{5}{2}\right)=0$
$x=5, x=\frac{5}{2}$
View full question & answer→Question 294 Marks
Solve the following equation: $\frac{ a }{ x - a }+\frac{ b }{ x - b }=\frac{2 c }{ x - c }$
Answer$\frac{a}{x-a}+\frac{b}{x-b}=\frac{2 c}{x-c}$
$\frac{a(x-b)+b(x-a)}{(x-a)(x-b)}=\frac{2 c}{x-c}$
$\frac{a x-a b+b x-a b}{x^2-a x-b x+a b}=\frac{2 c}{x-c}$
$\frac{(a+b) x-2 a b}{x^2-(a+b) x+a b}=\frac{2 c}{x-c}$
$\{(a+b) x-2 a b\}(x-c)=2 c\left\{x^2-(a+b) x+a b\right\}$
$(a+b) x^2-2 a b x-c(a+b) x+2 a b c=2 c x^2-2 c(a+b) x+2 a b c$
$(a+b) x^2-[2 a b+c(a+b)] x+2 a b c=2 c x^2-2 c(a+b) x+2 a b c$
$(a+b-2 c) x^2=(2 a b+a c+b c-2 c a-2 b c) x$
$(a+b-2 c) x^2=(2 a b-a c-b c) x$
$x=0, x=\frac{2 a b-a c-b c}{a+b-2 c}$
View full question & answer→Question 304 Marks
Solve the following equation: $\frac{1}{( x -1)(x-2)}+\frac{1}{( x -2)( x -3)}+\frac{1}{( x -3)( x -4)}=\frac{1}{6}$
Answer$\frac{1}{( x -1)(x-2)}+\frac{1}{( x -2)( x -3)}+\frac{1}{( x -3)( x -4)}=\frac{1}{6}$
$\frac{( x -3)( x -4)+( x -1)( x -4)+( x -1)( x -2)}{( x -1)( x -2)( x -3)( x -4)}=\frac{1}{6}$
$\frac{ x ^2-3 x -4 x +12+ x ^2- x -4 x +4+ x ^2- x -2 x +2}{( x -1)( x -2)( x -3)( x -4)}=\frac{1}{6}$
$\frac{3 x ^2-15 x +18}{( x -1)( x -2)( x -3)( x -4)}=\frac{1}{6}$
$\frac{3\left( x ^2-5 x +6\right)}{( x -1)( x -2)( x -3)( x -4)}=\frac{1}{6}$
$\frac{3( x -3)( x -2)}{( x -1)( x -2)( x -3)( x -4)}=\frac{1}{6}$
$\frac{3}{(x-1)(x-4)}=\frac{1}{6}$
$x^2-5 x+4=18$
$x^2-5 x-14=0$
$x^2+2 x-7 x-14=0$
$x(x+2)-7(x+2)=0$
$(x+2)(x-7)=0$
$x=-2, x=7$
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