Find x, if f(x)=g(x) wheref(x)=x-3, g(x)=5-x - Vidyadip

Question

Find $x$, if $f(x)=g(x)$ where$f(x)=\sqrt{x}-3, g(x)=5-x$

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Answer

$ f(x)=\sqrt{x}-3, g(x)=5-x$
$f(x)=g(x)$
$\therefore \sqrt{x}-3=5-x$
$\therefore \sqrt{x}=5-x+3$
$\therefore \sqrt{ } x=8-x $
on squaring, we get
$ \mathrm{x}=64+\mathrm{x}^2-16 \mathrm{x}$
$\therefore \mathrm{x}^2-17 \mathrm{x}+64=0$
$\therefore \mathrm{x}=\frac{17 \pm \sqrt{(-17)^2-4(64)}}{2}$
$\therefore \mathrm{x}=\frac{17 \pm \sqrt{289-256}}{2}$
$\therefore \mathrm{x}=\frac{17 \pm \sqrt{33}}{2} $

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