Question

# (x + 2)(x2 – 2x +1) Solution of - 20 is –4+ 3x – x2 (A) x € (-, -2] U{1} (B) x € (-0, -2] (C) x € (-0, -3] U{1} (D) x € (-0, -1] U {2}

Solution

$\frac{(x+2)({x}^{2}\u20132x+1)}{-4+3x\u2013{x}^{2}}\ge 0\phantom{\rule{0ex}{0ex}}\frac{\left(x+2\right){(x-1)}^{2}}{-({x}^{2}-3x+4)}\ge 0\Rightarrow \frac{\left(x+2\right){(x-1)}^{2}}{+({x}^{2}-3x)+4}\le \phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}x\in \left(-\infty ,-2\right)\cup \left\{1\right\}\phantom{\rule{0ex}{0ex}}\mathit{O}\mathit{p}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathbf{\left(}\mathit{A}\mathbf{\right)}\phantom{\rule{0ex}{0ex}}$