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Find the roots of the following quadratic equations (if they exist) by the method of completing the square. 1. {{x}^{2}}-4\sqrt{2x}+6=0
Class 10 | ICSE | Maths | Quadratic Equations | RD Sharma
Find the roots of the following quadratic equations (if they exist) by the method of completing the square. 1. {{x}^{2}}-4\sqrt{2x}+6=0

Quadratic is a type of problem which deals with a variable multiplied by itself- an operation also known as squaring.

Solution:

 Given equation,

{{x}^{2}}-4\sqrt{2x}+6=0

{{x}^{2}}-2\times x\times 2\sqrt{2}+{{\left( 2\sqrt{2} \right)}^{2}}-{{\left( 2\sqrt{2} \right)}^{2}}+6=0

{{\left( x-2\sqrt{2} \right)}^{2}}={{\left( 2\sqrt{2} \right)}^{2}}-6

{{\left( x-2\sqrt{2} \right)}^{2}}=\left( 4\times 2 \right)-6=8-6

{{\left( x-2\sqrt{2} \right)}^{2}}=2

\left( x-2\sqrt{2} \right)=\pm \sqrt{2}

\left( x-2\sqrt{2} \right)=\sqrt{2}orx=-\sqrt{2}+2\sqrt{2}

x=\sqrt{2}+2\sqrt{2}orx=-\sqrt{2}+2\sqrt{2}

\Rightarrow x=3\sqrt{2}oex=\sqrt{2}

Thus, the roots of the given quadratic equation are x=3\sqrt{2} and x=\sqrt{2}

 

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