Question

Solve the following equations

$16x-\frac{10}{x}=27$

$\frac{1}{x}-\frac{1}{x-2}=3,x\ne 0,2$

$x-\frac{2}{x}=3,x\ne 0$

Answer 1

$16x-\frac{10}{x}=27$

$16x^2-10=27x$

$16x^2-27x-10=0$

$16x^2-32x+5x-10=0$

$16x(x-2)+5(x-2)=0$

$x=\frac{-5}{16},+2$

$\frac{1}{x}-\frac{1}{x-2}=3$

$\Rightarrow \frac{x-2-x}{x^2-2x}=3$

$-2=3x-6x$

$3x^2-6x+2=0$

Roots $=\frac{6\pm \sqrt{3.6-4\times 2\times }}{2\times 3}$

$=\frac{6\pm \sqrt{12}}{6}$

$x-\frac{2}{x}=3$

$x^2-2=3x$ $\Rightarrow x^2-2x-x-2=0$

Roots $=\frac{3\pm \sqrt{9-4\times 1\times (-2)}}{2\times 1}$

$=\frac{3\pm \sqrt{17}}{2}$.