Solve the following quadratic equations by factorization: a x-b +… - Vidyadip

Question

Solve the following quadratic equations by factorization:
$\frac{\text{a}}{\text{x}-\text{b}}+\frac{\text{b}}{\text{x}-\text{a}}=2$

✓

Answer

$\frac{\text{a}}{\text{x}-\text{b}}+\frac{\text{b}}{\text{x}-\text{a}}=2$
$\Rightarrow\frac{\text{a}(\text{x}-\text{a})+\text{b}(\text{x}-\text{b})}{(\text{x}-\text{a})(\text{x}-\text{b})}=2$
$\Rightarrow ax - a^2 + bx - b^2 = 2x^2 - 2ax - 2bx + 2ab$
$\Rightarrow 2x^2 - 2ax - ax - 2bx - bx + a^2 + b^2 + 2ab = 0$
$\Rightarrow 2x^2 - 3x(a + b) + (a + b)^2 = 0$
$\Rightarrow 2x^2 - 2x(a + b) - x(a + b) + (a + b)^2= 0$
$\Rightarrow 2x[x - (a + b)] - (a + b)[x - (a + b)] = 0$
$\Rightarrow [2x - (a + b)] [(x - a + b)] = 0$
$\Rightarrow\text{x}=\frac{\text{a}+\text{b}}{2}$ or $x = a + b$

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→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

The following table shows the daily supply of electricity to different places in a town. Show the information by a pie diagram.

Places	Factories	Houses	Roads	Shops	Offices	Others
Supply of electricity (Thousand units)	24	14	7	5	6	4

While landing at an airport, a pilot made an angle of depression of 20°. Average speed of the plane was 200 km/hr. The plane reached the ground after 54 seconds. Find the height at which the plane was when it started landing. (sin 20° = 0.342)

Two men are on opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30° and 45° respectively. If the height of the tower is 50 metres, find the distance between the two men. $\big[\text{Take}\sqrt{3}=1.732\big]$

Using the distance formula, show taht the given points are collinear:
(6, 9), (0, 1) and (-6, -7)

Show that points $\mathrm{A}(-3,2), \mathrm{B}(1,-2)$ and $\mathrm{C}(9,-10)$ are collinear.

Show that the points (-3, -3), (3, 3) and $(-3\sqrt{3},3\sqrt{3})$ are the vertices of an equilateral triangle.

A solid is composed of a cylinder with hemispherical ends. If the length of the whole solid is 108cm and the diameter of the cylinder is 36cm, find the cost of polishing the surface at the rate of 7 paise per $cm^2.$

If $\sec\theta=\frac{5}{4},$ find the value of $\frac{\sin\theta-2\cos\theta}{\tan\theta-\cot\theta}.$

A chord PQ of a circle with radius 15 cm subtends an angle of 60° with the centre of the circle. Find the area of the minor as well as the major segment. (π = 3.14)

Solve the following quadratic equation.
$(2 x+3)^2=25$