Question

Solve the following quadratic equation:

1/(a+ b+ x) = 1/a +1/b +1/x , a+b ≠ 0 

Answer 1

\(\frac 1{a +b+ x} = \frac 1a + \frac 1b + \frac 1x\)

⇒ \(\frac 1{a + b + x} = \frac{bx + ax + ab}{abx}\)

⇒ abx = abx + a²x + a²b + b²x + abx + ab² + bx² + ax² + abx

⇒ x²(a + b) + x(2ab + a² + b²) + (a²b + ab²) = 0

⇒ x²(a + b) + x(a + b)² + ab(a + b) = 0

⇒ x² + x(a + b) + ab = 0

⇒ x² + ax + bx + ab = 0

⇒ (x + a)(x + b) = 0

∴ x = −a, x = −b

Answer 2

1/(a+ b+ x) = 1/a +1/b +1/x ,