Question

Solve the equation :-
1) (x+a/x-a)2 - 5(x+a/x-a) + 6 = 0
​

Answer 1

Answer:

$\longmapsto$ $\bigg(\dfrac{x + a}{x - a}\bigg)^{2} - 5\bigg(\dfrac{x + a}{x - a}\bigg)$ + 6 = 0

Let, $\dfrac{x + a}{x - a}$ = y.

Hence, the given equation is,

⇒ y²- 5y + 6 = 0

⇒ y²- 3y - 2y + 6 = 0

⇒y( y - 3 ) - 2( y - 3 ) = 0

⇒ ( y - 3 ) ( y - 2 ) = 0

⇒ y - 3 = 0 ; y - 2 = 0

➠ y = 3, y = 2

Now, if y = 3, then $\dfrac{x + a}{x - 3}$ = 4

↦ 3(x - a) = x + a

↦ 3x - 3a = x + a

↦3x - x = 3a + a

↦ 2x = 4a

↦ x = $\dfrac{4a}{2}$

➡ x = 2a

Again, of y = 2, then $\dfrac{x + a}{x - a}$ = 2

➛ 2(x - a) = x + a

➛2x - 2a = x + a

➛2x - x = 2a + a

➡ x = 3a

∴ Then, required solution is x = 2a, 3a.

Answer 2

Answer:

Then required solution is x = 2a, 3a