Question : If $\sqrt{x}=\sqrt{3}-\sqrt{5}$, then the value of $x^2-16x+6$ is:
Option 1: $0$
Option 2: $-2$
Option 3: $2$
Option 4: $4$
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Correct Answer: $2$
Solution :
Given: $\sqrt{x}=\sqrt{3}-\sqrt{5}$
By squaring both the sides, we get,
$x=3+5-2\sqrt{15}$
⇒ $x-8=-2\sqrt{15}$
Again, squaring both the sides, we get,
$x^2-16x+64=60$
⇒ $x^2-16x+4=0$
$\therefore x^2-16x+6=2$
Hence, the correct answer is $2$.
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