Question

Let $S=x: x∈R$ and \left(\sqrt{3}+\sqrt{2})^{x^2-4}+(\sqrt{3}-\sqrt{2})^{x^2-4}=10\right\\}Then $n(S)$ is equal to

• A. 2
• B. 4
• C. 0
• D. 6

Answer 1

Answer: (B)

4

Answer 2

The correct answer is (B) : 4
$\text{Let }(\sqrt3+\sqrt2)^{x^{2}−4}=t$
$t+\frac{1}{t}=10$
$⇒t=5+2\sqrt6, 5−2\sqrt6$
$⇒(\sqrt3+\sqrt2)^{x^{2}−4}=5+2\sqrt6, 5−2\sqrt6$
$⇒x^2−4=2, −2$ or $x^2 =6, 2$
$⇒x=±\sqrt2, ±\sqrt6$