Using the properties of proportion, solve for x, given. x^4+1 2 x… - Vidyadip

Question

Using the properties of proportion, solve for x, given.
$\frac{x^4+1}{2 x^2}=\frac{17}{8}$

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Answer

$\frac{x^4+1}{2 x^2}=\frac{17}{8}$
Using Componendo and Dividendo
$\frac{x^2+1+2 x^2}{x^4+1-2 x^2}=\frac{17+8}{17-8} $
$ \Rightarrow \frac{\left(x^2+1\right)^2}{\left(x^2-1\right)^2}=\frac{25}{9}$
$\Rightarrow \frac{x^2+1}{x^2-1}=\frac{5}{3} \ldots$ (taking square root on both the sides)
Again applying Componendo and Dividendo
$\frac{x^2+1+x^2-1}{x^2+1-x^2+1}=\frac{5+3}{5-3}$
$ \frac{2 x^2}{2}=\frac{8}{2} $
$ \Rightarrow x^2-4 \\ \Rightarrow x= \pm 2 .\end{array}$

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