Question

# The number of the integral solutions of 32 +9< (x + 3)2 < 8x + 25 is (A) 1 (B) 2 (C) 3 (D) None of these

Solution

$-{x}^{2}-3x+2=0(xispositive)\phantom{\rule{0ex}{0ex}}x=\frac{+3\pm \sqrt{9-8}}{2}\phantom{\rule{0ex}{0ex}}=\frac{3\pm 1}{2}\phantom{\rule{0ex}{0ex}}x=\frac{3+1}{2}\frac{3-1}{2}\phantom{\rule{0ex}{0ex}}\mathit{x}\mathbf{=}\mathbf{2}\mathbf{,}\mathbf{}\mathbf{1}\phantom{\rule{0ex}{0ex}}\mathbf{\therefore}\mathbf{}No.ofrealrootsofgiveneq.is2\phantom{\rule{0ex}{0ex}}\mathbf{\therefore}\mathit{o}\mathit{p}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathbf{\left(}\mathit{b}\mathbf{\right)}\mathbf{}\mathit{i}\mathit{s}\mathbf{}\mathit{c}\mathit{o}\mathit{r}\mathit{r}\mathit{e}\mathit{c}\mathit{t}\mathbf{}$