Download App

Quadratic Equations — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsQuadratic Equations4 Marks
Question
Solve the following quadratic equations by factorization:
$\frac{5+\text{x}}{5-\text{x}}-\frac{5-\text{x}}{5+\text{x}}=3\frac{3}{4},$ $\text{x}\neq5,-5$
✓

Answer

$\frac{5+\text{x}}{5-\text{x}}-\frac{5-\text{x}}{5+\text{x}}=3\frac{3}{4}$
$\frac{(5+\text{x})^2-(5-\text{x})^2}{(5-\text{x})(5+\text{x})}=\frac{15}{4}$
$\frac{25+\text{x}^2+10\text{x}-25-\text{x}^2+10\text{x}}{25-\text{x}^2}=\frac{15}{4}$
$\frac{20\text{x}}{25-\text{x}^2}=\frac{15}{4}$
$ \Rightarrow 80 x=375-15 x^2 $
$ \Rightarrow 15 x^2+80 x-375=0 $
$ \Rightarrow 3 x^2+16 x-75=0 $
$ \Rightarrow 3 x^2+25 x-9 x-75=0 $
$ \Rightarrow x(3 x+25)-3(3 x+25)=0 $
$ \Rightarrow(x-3)(3 x+25)=0$
$\text { Either } x-3=0$
$\therefore x = 3$
or $3x + 25 = 0$
$⇒ 3x = -25$
$\text{x}=-\frac{25}{3}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Questions" from Quadratic Equations→Quadratic Equations — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

Find the area of quadrilateral $PQRS$ whose vertices are $P(-5, -3), Q(-4, -6), R(2, -3)$ and $S(1, 2)$
→
If $AB, AC, PQ$ are tangents in the given figure and $AB = 5\ cm$, find the perimeter of $\triangle\text{APQ}$.
→
Prove that the square of any positive integer is of the form $3m$ or, $3m + 1$ but not of the from $3m + 2.$
→
For what values of $k$ are points $A(8,1), B(3,-2 k)$ and $C(k,-5)$ collinear.
→
A tree standing on a horizontal plane is leaning towards east. At two points situated at distances a and b exactly due west on it, the angles of elevation of the top are respectively $\alpha$ and $\beta.$ Prove that the height of the top from the ground is, $\frac{(\text{b}-\text{a})\tan\alpha\tan\beta}{\tan\alpha-\tan\beta}.$
→
In the given figure, $AB || CD$, if $OA = 3x - 19, OB = x - 4, OC = x - 3$ and $OD = 4$, find $x.$
→
Calculate the missing frequency from the following distribution, it being given that the median of the distribution is $24.$
Class $0-10$ $10-20$ $20-30$ $30-40$ $40-50$
Frequency $5$ $25$ $?$ $18$ $7$
→
If $(\text{cosec }\theta+\sin\theta)=\text{a}^3$ and $(\sec\theta-\cos\theta)=\text{b}^3,$ prove that $\big(\text{a}^2\text{b}^2\big)\big(\text{a}^2+\text{b}^2\big)=1.$
→
Find the values of a and b for which the following system of equations has infinitely many solutions:
$2x + 3y = 7$
$(a - 1)x + (a + 2)y = 3a$
→
If $\triangle\text{ABC}\sim\triangle\text{DEF}$ such that $2 A B=D E$ and $B C=6 cm$, find $E F$.
→