Question

If `25x^2 + 1/(4x^2) = 20,` find the value of `5x + 1/(2x)`

Answer 1

Given: `25x^2 + 1/(4x^2) = 20,`

Here, let A = `5x + 1/(2x)`

Now, squaring both sides:

`(A)^2 = (5x + 1/(2x))^2`

`(A)^2 = 25x^2 + 1/(4x^2) + 2(5x) (1/(2x))`

`(A)^2 = 25x^2 + 1/(4x^2) + 5`

(A)² = 20 + 5

(A)² = 25

∴ A = `+-sqrt25`

∴ A = ±5