Solve the following quadratic equation. 1 x+5 = 1 x^2 - Vidyadip

Question

Solve the following quadratic equation.
$\frac{1}{x+5} = \frac{1}{x^2}$

✓

Answer

$x ^2= x +5 $
$ \Rightarrow x ^2- x -5=0 $
$ \Rightarrow x ^2- x -5=0 \text { compare with } ax ^2+ bx + c =0$
$ \Rightarrow a =1, b=-1 \text { and } c =-5$
$ \therefore b ^2-4 ac =-1^2-4(1)(-5) $
$ =1+20 $
$ =21$
$ x =\frac{- b \pm \sqrt{ b ^2-4 ac }}{2 a } $
$ \Rightarrow x =\frac{1 \pm \sqrt{21}}{2 \times 1} $
$ \Rightarrow x =\frac{1 \pm \sqrt{21}}{2} $
$ \Rightarrow x =\frac{1+\sqrt{21}}{2} \text { or } x =\frac{1+\sqrt{21}}{2}$

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