Question

x²-4✓2x+6=0
find the roots of the following quadratic equations by the method of completing the square​

Answer 1

Question -

Find the roots of the following quadratic equations by the method of completing the square

$1) {x}^{2} - 4 \sqrt{2}x + 6 = 0$

Solution -

We have,

${x}^{2} - 4 \sqrt{2} x + 6 = 0$

${x}^{2} - 2 \times x \times 2 \sqrt{2} + {(2 \sqrt{2}) }^{2} - {(2 \sqrt{2} )}^{2} + 6 = 0$

${(x - 2 \sqrt{2} )}^{2} - {(2 \sqrt{2}) }^{2} + 6 = 0$

${(x - 2 \sqrt{2} )}^{2} = {(2 \sqrt{2} )}^{2} - 6$

${(x - 2 \sqrt{2}) }^{2 } = (4 \times 2) - 6$

${(x - 2 \sqrt{2}) }^{2} = 8 - 6$

${(x - 2 \sqrt{2} )}^{2} = 2$

$x - 2 \sqrt{2} = \frac{ + }{ - } 2$

$x - 2 \sqrt{2} = 2 \: or \: x - 2 \sqrt{2} = - 2$

$x = 3 \sqrt{2} \: or \: \: x = \sqrt{2}$

$\therefore \: x = \sqrt{2} \: and \: x = 3 \sqrt{2} \: are \: roots \: of \: the \: equation \: \: {x}^{2} - 4 \sqrt{2} x + 6 = 0$