Question

Solve for $x:5\sqrt{\frac{3}{x}}+7\sqrt{\frac{x}{3}}=22\frac{2}{3}$

Answer 1

$5\sqrt{\frac{3}{x}}+7\sqrt{\frac{x}{3}}=22\frac{2}{3}$

$5\sqrt{\frac{3}{x}}+7\sqrt{\frac{x}{3}}=\frac{68}{3}$

$\frac{15+7x}{\sqrt{x}}=\frac{68}{\sqrt{3}}$

$15\sqrt{3}+7\sqrt{3}x=68\sqrt{x}$

squaring on both sides, we get,

$675+147x^2+630x=4624x$

$147x^2-3994x+675=0$

$x=\frac{-(-3994)+\sqrt{{(-3994)}^2-4\cdot 147\cdot 675}}{2\cdot 147}:27$

$x=\frac{-(-3994)-\sqrt{{(-3994)}^2-4\cdot 147\cdot 675}}{2\cdot 147}:\frac{25}{147}$

$\therefore x=27,\frac{25}{147}$