Question

answer the above question ​

Answer 1

Answer:

its the answer of questions

Answer 2

√2x² + 7x + 5√2 $\; \;$

We have to solve above equation .

We have many methods like completing the square method , Middle term splitting method , ... etc .

Let's go with middle term splitting method ,

➠ √2 x² + 7x + 5√2

On splitting the middle term , we get ,

➠ √2 x² + 2x + 5x + 5√2

➠ √2 x ( x + √2 ) + 5 ( x + √2 )

➠ ( x + √2 ) ( √2 x + 5 )

So ,

➠ ( x + √2 ) ( √2 x + 5 ) = 0

➠ x = - √2  ;  x = - ⁵/√2

Alternate Method :

Completing the square method :

$\sf \sqrt{2}x^2+7x+5\sqrt{2}=0\\\\\to \sf \dfrac{\sqrt{2}x^2}{\sqrt{2}}+\dfrac{7x}{\sqrt{2}}+\dfrac{5\sqrt{2}}{\sqrt{2}}=0\\\\\to \sf x^2+2.x.\dfrac{7}{2(\sqrt{2})}+5=0$

$\to \sf x^2+2.x.\dfrac{7}{2\sqrt{2}}+\bigg(\dfrac{7}{2\sqrt{2}}\bigg)^2-\bigg(\dfrac{7}{2\sqrt{2}}\bigg)^2+5=0$

$\to \sf \bigg(x+\dfrac{7}{2\sqrt{2}}\bigg)^2=\dfrac{49}{8}-5\\\\\to \sf \bigg(x+\dfrac{7}{2\sqrt{2}}\bigg)^2=\dfrac{9}{8}\\\\\to \sf x+\dfrac{7}{2\sqrt{2}}=\pm \dfrac{3}{2\sqrt{2}}\\\\\to \sf x=\dfrac{-7\pm 3}{2\sqrt{2}}$

$\to \sf x=-\dfrac{4}{2\sqrt{2}}\ ;\ x=-\dfrac{10}{2\sqrt{2}}\\\\\to \sf x=-\dfrac{2}{\sqrt{2}}\ ;\ x=-\dfrac{5}{\sqrt{2}}\\\\\leadsto \sf \orange{x=-\sqrt{2}}\ ;\ \green{x=-\dfrac{5}{\sqrt{2}}}\ \; \bigstar$