Question

`sqrt2x^2+7x+5sqrt2=0` 

 

Answer 1

We write, `7x=5x+2x  as  sqrt2x^2xx5sqrt2=10x^2=5x xx  2x` 

∴` sqrt2x^2+7x+5sqrt2=0` 

⇒` sqrt2x^2+5x+2x+5sqrt2=0` 

⇒` x(sqrt2x+5 )+sqrt2 (sqrt2x+5)=0` 

⇒`(sqrt2x+5)(x+sqrt2)=0` 

⇒`x+sqrt2=0  or  sqrt2x+5=0` 

⇒`x=-sqrt2  or  x=-5/sqrt2=-(5sqrt2)/2` 

Hence, the roots of the given equation are `-sqrt2` and `(-5sqrt2)/2`