Question

solve by factorisation method and use d=b square-4ac and then -b plus minus under root of d divided by 2× a​

Answer 1

Solution:-

Given equation is

$\to \bf\sqrt{2}x {}^{2} + 7x + 5 \sqrt{2} = 0$

So, compare with ax² + bx + c = 0

$\to \bf \: a = \sqrt{2} \: \: \: \: b = 7 \: \: and \: c = 5 \sqrt{2}$

Use quadratic formula to solve :-

$\to \bf \: x = \frac{ - b \pm \sqrt{b {}^{2} - 4ac} }{2a}$

Put the value , we get

$\to \bf \: x = \frac{ - 7 \pm \sqrt{(7) {}^{2} - 4 \times 5 \sqrt{2} \times \sqrt{2} } }{2 \sqrt{2} }$

$\to \bf \: x = \frac{ - 7 \pm\: \sqrt{49 - 4 \times 10} }{2 \sqrt{2} }$

$\to \bf \: x = \frac{ - 7 \pm \sqrt{9} }{2 \sqrt{2} }$

$\to \bf \: x = \frac{ - 7 + 3}{2 \sqrt{2} } \: and \: \frac{ - 7 - 3}{2 \sqrt{2} }$

$\to \bf \: x = \frac{ - 4}{2 \sqrt{2} \: } \: and \: \: \frac{ - 10}{2 \sqrt{2} }$

$\to \bf \: x = \frac{ - 2}{ \sqrt{2} } \: \: and \: \frac{ - 5}{ \sqrt{2} }$

Now rationalize the value of so we get final value of x

$\to \bf \: x = \frac{ - 2 \times \sqrt{2} }{ \sqrt{2} \times \sqrt{2} } \: and \: \frac{ - 5 \times \sqrt{2} }{ \sqrt{2} \times \sqrt{2} }$

$\to \bf \: x = \frac{ - 2 \sqrt{2} }{2} \: \: and \: \: \frac{ - 5 \sqrt{2} }{2}$

So value of x is

$\to \bf \: x = \: - \sqrt{2} \: \: and \: \frac{ - 5 \sqrt{2} }{2}$