Question

$\sqrt{2 {x}^{2} } + 7x + 5 \sqrt{2} = 0$
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Answer 1

Answer:

$true$

Step-by-step explanation:

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Answer 2

Given,

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

To find:-

• The value of x.

Solution:-

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

$\implies \sqrt{2} {x}^{2} + 2x + 5x + 5 \sqrt{2} = 0$

$\implies \sqrt{2} x(x + \sqrt{2} ) + 5(x + \sqrt{2} ) = 0$

$\implies ( \sqrt{2} x + 5)(x + \sqrt{2}) = 0$

Therefore,

Either

$\sqrt{2} x + 5 = 0$

Or,

$x + \sqrt{2} = 0$

Therefore,

$x = - \frac{5 }{ \sqrt{2} }$

$x = - \sqrt{2}$

Answer:-

The two solutions for the given equation are:-

$x = - \frac{5 }{ \sqrt{2} }$

$x = - \sqrt{2}$