Question

find the value of x of the given quadratic equation a÷x-b + b÷x-a = 2​

Answer 1

Answer: "= ^2 /²

a/x-b +b/x-a =2

a(x-a)+b(x-b)/(x-a)(x-b)=2

ax - a" + bx - b" = 2 (x-a) (x-b)

ax - a" + bx - b" = (2x-2a) (x-b)

ax - a" + bx - b" = 2x" - 2bx - 2ax + 2ab

-2x" + 3bx + 3ax - a" - b" - 2ab = 0

2x" - 3bx - 3ax + a" + b" +2ab = 0

2x" - 3 (a+b) x + (a+b)" = 0

2x" - 2(a+b)x - 1(a+b)x + (a+b)" = 0

2x [x - (a+b)] - (a+b) [x - (a+b)] = 0

(2x - a - b ) (x - a - b) = 0

Thus, either -

2x - a - b = 0

Therefore x = a+b / 2

or -

x - a - b = 0

Therefore x = a + b

Step-by-step explanation: