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Shalnov [3]
4 years ago
11

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

Mathematics
1 answer:
Semenov [28]4 years ago
4 0
<em>Solve: </em>\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}
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