Question

Solve: (1/x)+6 = 5/sqrt(x)

Answer 1

Solve: $\frac{1}{x} + 6 = \frac{5}{\sqrt{x}}$

Start by squaring both sides to eliminate the square root.
$(\frac{1}{x} + 6)^{2} = \frac{25}{x}$

Expand the left hand side.
$\frac{1}{x^{2}} + \frac{12}{x} + 36 = \frac{25}{x}$

Simplify.
$\frac{1}{x^{2}} - \frac{13}{x} + 36 = 0$
$\frac{1 - 13x + 36x^{2}}{x^{2}} = 0$

Solve for x.
$36x^{2} - 13x + 1 = 0$
$36x^{2} - 9x - 4x + 1 = 0$
$9x(4x - 1) - (4x - 1) = 0$

$(9x - 1)(4x - 1) = 0$
$\therefore x = \frac{1}{9}, \frac{1}{4}$