$x=\sqrt{30}-1$

Algebra Level 1

If $x=\sqrt{30}-1$ , the value of $\sqrt{x^2+4x-16}$ can be expressed as $\sqrt{a}+\sqrt{b}.$ What is $a+b?$

13 11 10 12

1 solution

Victor Loh
Mar 17, 2014

Substituting $x=\sqrt{30}-1$ into $x^{2}+4x-16$ , we have

$x^{2}+4x-16$

$=(\sqrt{30}-1)^{2}+4(\sqrt{30}-1)-16$

$=(30+1-2\sqrt{30})+(4\sqrt{30}-4)-16$

$=11+2\sqrt{30}$

Note that $(\sqrt{a}+\sqrt{b})^{2}=(a+b)+2\sqrt{ab}$ , hence we have

$a+b=11$

$ab=30$

and we are done.

it's good...

Jesrel Lood - 7 years, 2 months ago

hmm cool

Nafsin Rahman - 7 years, 2 months ago