Question

Solve the following equation.

`[(4x +1)^2 + ( 2x + 3)^2]/[4x^2 + 12x + 9] = 61/36`

Answer 1

` [(4x +1)^2 + ( 2x + 3)^2]/[4x^2 + 12x + 9] = 61/36`

⇒ ` [(4x +1)^2 + ( 2x + 3)^2]/[(2x)^2 + 2 (2x) (3) + 3^2] = 61/36`

⇒ ` ((4x +1)^2 + ( 2x + 3)^2)/(2x + 3)^2 = 61/36`

Applying dividendo, we get

⇒ `{(4x +1)^2 + ( 2x + 3)^2 - (2x + 3)^2}/( 2x + 3)^2 = (61 - 36)/36`

⇒ `[(4x + 1)^2]/[( 2x + 3 )^2] =  25/36`

Taking square root on both sides, we get

⇒ `( 4x + 1)/(2x + 3) = sqrt (25/36) = 5/6`

⇒ `(4x + 1)/(2x + 3) = 5/6`

⇒ `6(4x + 1) + 5(2x + 3)`

⇒ `24x + 6 = 10x + 15`

⇒ `24x - 10x = 15 - 6`

⇒ `14x = 9`

⇒ `x =9/14`

Thus, the solution of the given equation is x = `9/14`.