Question

Solve the following equations:
$\frac{3}{\sqrt{2x}}-\frac{\sqrt{2x}}{5}=5\frac{9}{10}$.

Answer 1

$\frac{3}{\sqrt{2x}}-\frac{\sqrt{2x}}{5}=5\frac{9}{10}$

Put $\sqrt{2x}=t$

$\frac{3}{t}-\frac{t}{5}=5\frac{9}{10}\frac{3}{t}-\frac{t}{5}=\frac{59}{10}\frac{15-t^2}{5t}=\frac{59}{10}\frac{15-t^2}{t}=\frac{59}{2}30-2t^2=59t30-2t^2-59t=02t^2+59t-30=02t^2-t+60t-30=0t(2t-1)+30(2t-1)=0(t+30)(2t-1)=0t=\frac{1}{2},-30\sqrt{2x}=t2x=t^{2}x=\frac{1}{2}{t}^{2}x={\frac{1}{2}\left(\frac{1}{2}\right)}^2=\frac{1}{8}x=\frac{1}{2}{(-30)}^2=\frac{900}{2}=450x=\frac{1}{8},450$