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# Find the roots of the following quadratic equations (if they exist) by the method of completing the square. x^2-(sqrt2+1)x+sqrt2=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-(sqrt2+1)x+sqrt2=0

#### Solution

We have been given that,

x^2-(sqrt2+1)x+sqrt2=0

Now take the constant term to the RHS and we get

x^2-(sqrt2+1)x=-sqrt2

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

x^2-(sqrt2+1)x+((sqrt2+1)/2)^2=((sqrt2+1)/2)^2-sqrt2

x^2+((sqrt2+1)/2)^2-2((sqrt2+1)/2)x=(3-2sqrt2)/4

(x-(sqrt2+1)/2)^2=(sqrt2-1)^2/2^2

Since RHS is a positive number, therefore the roots of the equation exist.

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

x-(sqrt2+1)/2=+-((sqrt2-1)/2)

x=(sqrt2+1)/2+-(sqrt2-1)/2

Now, we have the values of ‘x’ as

x=(sqrt2+1)/2+(sqrt2-1)/2=sqrt2

Also we have,

x=(sqrt2+1)/2-(sqrt2-1)/2=1

Therefore the roots of the equation are sqrt2and 1.

Is there an error in this question or solution?

#### 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-(sqrt2+1)x+sqrt2=0 Concept: Solutions of Quadratic Equations by Completing the Square.