Find the roots of the following quadratic equations (if they exist) by the method of completing the square.

$x^2 - 4\sqrt2 x + 6 = 0$

Given:

Given quadratic equation is $x^2 - 4\sqrt2 x + 6 = 0$.

To do:

We have to find the roots of the given quadratic equation.

Solution:

$x^2 - 4\sqrt2 x + 6 = 0$

$x^2 - 2\times 2\sqrt2 x  = -6$    ($2\times2\sqrt2=4\sqrt2$)

Adding $(2\sqrt2)^2$ on both sides completes the square. Therefore,

$x^2 - 2\times (2\sqrt2) x + (2\sqrt2)^2 = -6+(2\sqrt2)^2$

$(x-2\sqrt2)^2=-6+8$      (Since $(a-b)^2=a^2-2ab+b^2$)

$(x-2\sqrt2)^2=2$

$x-2\sqrt2=\pm \sqrt{2}$     (Taking square root on both sides)

$x=2\sqrt2+\sqrt2$ or $x=2\sqrt2-\sqrt2$

$x=3\sqrt2$ or $x=\sqrt2$

The values of $x$ are $3\sqrt2$ and $\sqrt2$.

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Updated on: 10-Oct-2022

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