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# Find the Roots of the Following Quadratic Equations (If They Exist) by the Method of Completing the Square. X^2-4sqrt2x+6=0 - Mathematics

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#### Question

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

x^2-4sqrt2x+6=0

#### Solution

We have been given that,

x^2-4sqrt2x+6=0

Now we take the constant term to the right hand side and we get

x^2-4sqrt2x=-6

Now add square of half of co-efficient of ‘x’ on both the sides. We have,

x^2 - 4sqrt2x+(2sqrt2)^2=(2sqrt2)^2-6

x^2+(2sqrt2)^2-2(2sqrt2)x=2

(x-2sqrt2)^2=2

Since right hand side is a positive number, the roots of the equation exist.

So, now take the square root on both the sides and we get

x-2sqrt2=+-sqrt2

x=2sqrt2+-sqrt2

Now, we have the values of ‘x’ as

x=2sqrt2+sqrt2=3sqrt2

Also we have,

x=2sqrt2-sqrt2=sqrt2

Therefore the roots of the equation are 3sqrt2 and sqrt2.

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#### APPEARS IN

RD Sharma Solution for Class 10 Maths (2018 (Latest))
Find the Roots of the Following Quadratic Equations (If They Exist) by the Method of Completing the Square. X^2-4sqrt2x+6=0 Concept: Solutions of Quadratic Equations by Completing the Square.