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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`.

  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: 1 | Page no. 26
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.4 | Q: 1 | 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^2-4sqrt2x+6=0` Concept: Solutions of Quadratic Equations by Completing the Square.
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