If $\sqrt{x} = \sqrt{3} - \sqrt{5}$, then the value of $x^2 - 16 x+ 6$ is :
Answer & explanation
Correct answer: option 3
$\sqrt{x} = \sqrt{3} - \sqrt{5}$
Squaring both sides
($\sqrt{x}$)2 = ($ \sqrt{3} - \sqrt{5}$)2
= x = 3 + 5 – 2√15
= x – 8 = -2√15
Again, squaring both sides
(x – 8)2 = (-2√15)2
= x2 + 64 – 16x = 4 × 15
= x2 + 4 – 16x = 0
= x2 – 16x + 6 = 2