Solve the following equations by using the method of completing t… - Vidyadip

Question

Solve the following equations by using the method of completing the square:
$ x^2-6 x+3=0 $

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Answer

$ x^2-6 x+3=0 $
$ \Rightarrow x^2-6 x=-3 $
$ \Rightarrow x^2-2 \times x \times 3+3^2=-3+3^2 \text { (Adding } 3^2 \text { on both sides) } $
$ \Rightarrow(x-3)^2=-3+9=6$
$\Rightarrow\text{x}-3=\pm\sqrt6$ (Taking square root on both sides)
$\Rightarrow\text{x}-3=\sqrt6$ or $\text{x}-3=-\sqrt6$
$\Rightarrow\text{x}=3+\sqrt6$ or $\text{x}=3-\sqrt6$
Hence, $3+\sqrt6$ and $3-\sqrt6$ are the roots of the given equation.

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