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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 `sqrt2`and 1.

  Is there an error in this question or solution?
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APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.4 | Q: 9 | Page no. 26
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.4 | Q: 9 | Page no. 26
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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` Concept: Solutions of Quadratic Equations by Completing the Square.
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