Question

Solve the following equation.

`[( 2x + 1)^2 + (2x - 1)^2]/[(2x + 1)^2 - (2x - 1)^2] = 17/8`

Answer 1

`[( 2x + 1)^2 + (2x - 1)^2]/[(2x + 1)^2 - (2x - 1)^2] = 17/8`

Applying componendo and dividendo, we get

`{[( 2x + 1)^2 + (2x - 1)^2] + [(2x + 1)^2 - (2x - 1)^2]}/{[( 2x + 1)^2 + (2x - 1)^2] - [(2x + 1)^2 - (2x - 1)^2]} = [17+8]/[17 - 8]`

⇒ `[2( 2x + 1)^2] /[2( 2x - 1)^2] = 25/9`

⇒ `(2x + 1)/( 2x - 1) = sqrt(25/9)`

⇒ `(2x + 1)/( 2x - 1) = 5/3`

⇒ `3(2x + 1) = 5(2x - 1)`

⇒ `6x + 3 = 10x - 5`

⇒ `10x - 6x = 5 + 3`

⇒ `4x = 8`

⇒ `x = 2`

Thus, the solution of the given equation is x = 2.