Correct Answer - Option 3 : 2
Calculation:
\((9 + 4√5)^{(x^2-3)} + (9- 4√5)^{(x^2-3)} = 18\) possible if and only if power of both the term are 1 or – 1 as (9 + 4√5)(9 + 4√5) = 1 & (9 + 4√5) + (9 + 4√5) = 18
\(⇒ (x^2-3) = 1
\)
\(⇒x^2 = 4\)
\(⇒(x^2-3) = -1 \)
\(⇒x^2 = 2\)
Therefore, x will take 4 Values 2, -2, √2, -√2 but there are only two integral value 2 and -2