Solve the following quadratic equation by factorization:

$3x^2-2\sqrt{6}x+2=0$

Given:

Given quadratic equation is $3x^2-2\sqrt{6}x+2=0$.

To do:

We have to solve the given quadratic equation.

Solution:

$3x^2-2\sqrt{6}x+2=0$

To factorise $3x^2-2\sqrt{6}x+2=0$, we have to find two numbers $m$ and $n$ such that $m+n=-2\sqrt6$ and $mn=3\times2=6$.

If $m=-\sqrt6$ and $n=-\sqrt6$, $m+n=-\sqrt6+(-\sqrt6)=-2\sqrt6$ and $mn=(-\sqrt6)(-\sqrt6)=6$.

$3x^2-\sqrt{6}x-\sqrt{6}x+2=0$

$\sqrt{3}x(\sqrt{3}x-\sqrt2)-\sqrt{2}(\sqrt{3}x-\sqrt2)=0$

$(\sqrt{3}x-\sqrt{2})(\sqrt{3}x-\sqrt2)=0$

$(\sqrt{3}x-\sqrt{2})^2=0$ 

$\sqrt{3}x-\sqrt{2}=0$

$\sqrt{3}x=\sqrt2$

$x=\frac{\sqrt2}{\sqrt3}$

$x=\sqrt{\frac{2}{3}}$

The values of $x$ is $\sqrt{\frac{2}{3}}$.

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Updated on: 10-Oct-2022

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