\(\sqrt{x}\) – \(\frac{6}{\sqrt{x}}\) = 1, find the value of x

Explanation

\(\sqrt{x}\) - \(\frac{6}{\sqrt{x}}\) = 1

Multiply through by \(\sqrt{x}\)

x - 6 = \(\sqrt{x}\)

x - \(\sqrt{x}\) = 6

let \(\sqrt{x}\) = q, then x = q\(^2\)

q\(^2\) - q - 6 = 0

q\(^2\) - 3q + 2q - 6 = 0

q(q - 3) + 2(q - 3) = 0

(q - 3)(q + 2) = 0

q = 3 or -2

but x =  q\(^2\), meaning, x = 9 or 4.