Question

If `9x^2 + 1/(4x^2) = 13,` find the value of `3x + 1/(2x)`.

Answer 1

Given: `9x^2 + 1/(4x^2) = 13,`

Let, A = `3x + 1/(2x)`

Now, squaring on both sides:

`(A)^2 = (3x + 1/(2x))^2`

`A^2 = 9x^2 + 1/(4x^2) + 2(3x)(1/(2x))`

`A^2 = 9x^2 + 1/(4x^2) + 3`

`A^2 = 13 + 3`

∴ `A^2 = 16`

∴ `A = +-sqrt16`

∴ A = ±4

Hence, `3x + 1/(2x) = +-4`