#### Question

Solve the following quadratic equations by factorization:

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

#### Solution

We have been given

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

`(x^2+a^2-2ax+x^2+b^2-2bx)/(x^2-(a+b)x+ab)=(a^2+b^2)/(ab)`

2abx^{2} - 2(ab)(a + b)x + ab(a^{2} + b^{2}) = (a^{2} + b^{2})x^{2} - (a + b)(a^{2} + b^{2})x + ab(a^{2} + b^{2})

(a - b)^{2}x^{2} - (a + b)(a - b)^{2}x = 0

x(a - b)^{2}(x - (a + b)) = 0

Therefore,

x(a - b)^{2} = 0

x = 0

or,

x - (a + b) = 0

x = a + b

Hence, x = 0 or x = a + b.

Is there an error in this question or solution?

#### APPEARS IN

Solution Solve the Following Quadratic Equations by Factorization: `(X-a)/(X-b)+(X-b)/(X-a)=A/B+B/A` Concept: Solutions of Quadratic Equations by Factorization.