Question

please solve this .Its urgent
(x+a/x-a)^2-5(x+a/x-a)+6=0​

Answer 1

Answer:

x = 2a  OR  x = 3a

Step-by-step explanation:

Put u = (x+a) / (x-a).

The equation is

u² - 5u + 6 = 0

=> ( u - 2 ) ( u - 3 ) = 0

=> u = 2 or u = 3

Writing x in terms of u:

u = ( x + a ) / ( x - a )

=> ux - ua = x + a

=> ( u - 1 ) x = a ( u + 1 )

=> x = a ( u + 1 ) / ( u - 1 ).

If u = 2, then x = 3a.

If u = 3, then x = 4a/2 = 2a.

Answer 2

let (x+a/x-a) be any variable, say 'y'......

then,

y^2 - 5y + 6=0

y^2 - 3y -2y + 6=0

y(y-3) -2(y-3)=0

(y-3) (y-2)=0

hence,

y=2,3

now,

y=x+a/x-a

x+a/x-a = 2

x+a = 2(x-a)

x+a = 2x-2a

2a+a = 2x-x

x= 3a

Similarly,

x+a/x-a = 3

x+a = 3(x-a)

x+a = 3x-3a

3a+a = 3x-x

4a = 2x

x=2a

therefore we get two solutions for x, i.e.,

x=2a and x=3a..

hope it helps you....

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