Question

Fectorice √2 x2+x- √2​

Answer 1

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Factorise

$\mathrm{ \sqrt{2} {x}^{2} + x - \sqrt{2} }$

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$\rightarrow \bf \sqrt{2} {x}^{2} + x - \sqrt{2} = 0 \\ \\ \rightarrow \bf \sqrt{2} {x}^{2} + 2x - x - \sqrt{2} = 0 \\ \\ \rightarrow \bf \sqrt{2} x(x + \sqrt{2} ) - 1(x + \sqrt{2} ) = 0 \\ \\ \rightarrow \bf ( \sqrt{2} x - 1)(x + \sqrt{2} ) = 0$

Hence,

$\boxed{ \bf{x = \frac{1}{ \sqrt{2} }}}$

And

$\boxed{ \bf \: x = - \sqrt{2} }$