Question

Find the roots of the following quadratic equation( if they exist)by the method if completing the square. x²-4√2x+6=0.... please don't spam​

Answer 1

Given:-

• x² - 4√2x + 6 = 0

To find:-

• Find the roots of the equation.?

Solutions:-

• x² - 4√2x + 6 = 0

Now, the constant term to the right hand side, we get.

=> x² - 4√2x = - 6

Now, add square of half of co - efficient of x on both the side.

=> x² - 4√2x + (2√2)² = (2√2)² - 6

=> x² + (2√2)² - 2(2√2)x = 2

=> x² + (2√2)² - 2(2√2)x = 2

=> (x - 2√2)² = 2

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

So, the square root on both the sides and we get.

=> x - 2√2 = +,- √2

=> x = 2√2 +,- √2

Also, we have the values of x.

=> x = 2√2 + √2

=> x = 3√2

Also,

=> x = 2√2 - √2

=> x = √2

Hence, the roots of the equation are 3√2 and √2.

Answer 2

Plz tell that if it works or not!!!