Question

Solve the following inequality:
$\frac{\sqrt{2x^2+15x-17}}{10-x}⩾0.$

Answer 1

$2x^2+15x-17\ge 02x^2+17x-2x-17\ge 0(x-1)(2x-17)\ge 0x\in (-\infty ,\frac{-17}{2})\cup (1,\infty )\frac{\sqrt{2x^2+15x-17}}{10-x}\ge 0\frac{2x^2+15x-17}{{(x-10)}^2}\ge 0\frac{(x-1)(2x+17)}{{(x-10)}^2}\ge 0x\in (-\infty ,\frac{-17}{2}]\cup [1,10)\cup (10,\infty )x\in (-\infty ,\frac{-17}{2}]\cup [1,\infty )-\left\{10\right\}$