Question
Solve the following quadratic equations by factorization:
$\frac{1}{\text{x}}-\frac{1}{\text{x}-2}=3,$ $\text{x}\neq0,2$
$\frac{1}{\text{x}}-\frac{1}{\text{x}-2}=3,$ $\text{x}\neq0,2$
✓
Answer
$\frac{1}{\text{x}}-\frac{1}{\text{x}-2}=3$ $(\text{x}\neq0,2)$
$\frac{\text{x}-2-\text{x}}{\text{x}(\text{x}-2)}=3$
$\Rightarrow\frac{-2}{\text{x}^2-2\text{x}}=3$
$\Rightarrow 3x^2 - 6x = -2$
$\Rightarrow 3x^2 - 6x + 2 = 0$
Here $a = 3, b = -6, c = 2$
$D = b^2 - 4ac = (-6)^2 - 4 \times 3 \times 2$
$= 36 - 24 = 12$
$\therefore\text{x} = {-\text{b} \pm \sqrt{\text{b}^2-4\text{ac}} \over 2\text{a}}$
$\text{x}={-(-6) \pm \sqrt{12} \over 2\times3}$
$\text{x}={6 \pm2 \sqrt{3} \over6}$
$\text{x}=\frac{2(3\pm\sqrt{3})}{6}$
$\text{x}=\frac{3\pm\sqrt{3}}{3}$
$\frac{\text{x}-2-\text{x}}{\text{x}(\text{x}-2)}=3$
$\Rightarrow\frac{-2}{\text{x}^2-2\text{x}}=3$
$\Rightarrow 3x^2 - 6x = -2$
$\Rightarrow 3x^2 - 6x + 2 = 0$
Here $a = 3, b = -6, c = 2$
$D = b^2 - 4ac = (-6)^2 - 4 \times 3 \times 2$
$= 36 - 24 = 12$
$\therefore\text{x} = {-\text{b} \pm \sqrt{\text{b}^2-4\text{ac}} \over 2\text{a}}$
$\text{x}={-(-6) \pm \sqrt{12} \over 2\times3}$
$\text{x}={6 \pm2 \sqrt{3} \over6}$
$\text{x}=\frac{2(3\pm\sqrt{3})}{6}$
$\text{x}=\frac{3\pm\sqrt{3}}{3}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Is the given sequence $a, 2a, 3a, 4a,...$ forms an$ AP$? If it forms an $AP$, then find the common difference d and write the next three terms.
→The angles of a quadrilateral are in A.P. whose common difference is 10º. Find the numbers.
If the area of the base of a right circular cone is $3850 cm^2$ and its height is 84cm, then find the slant height of the cone.
→Prove the following identities:
$\sin\theta(1+\tan\theta)+\cos\theta(1+\cot\theta)=(\sec\theta+\text{cosec }\theta)$
→$\sin\theta(1+\tan\theta)+\cos\theta(1+\cot\theta)=(\sec\theta+\text{cosec }\theta)$
Evaluate the following:
$\cot^230^\circ-2\cos^260^\circ-\frac{3}{4}\sec^245^\circ-4\sec^230^\circ$
→$\cot^230^\circ-2\cos^260^\circ-\frac{3}{4}\sec^245^\circ-4\sec^230^\circ$
For what value of k, the following pair of linear equation has infinitely many solutions?
→$10x + 5y - (k - 5) = 0$
$20x + 10y - k = 0$
A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC
Find the area and perimeter of a square plot of land whose diagonal is 24m long. $\big[\text{Take}\sqrt{2}=1.41\big]$
→On a horizontal plane there is vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are 60° and 30° respectively. Find the height of the tower and the flag pole mounted on it.
Which term of the AP 72, 68, 64, 60, ..... is 0?