Question

Minimum value of $\lambda$ for which the equation $9a^{2x}-(\lambda +2)a^x+4=0$ . $a>1$ has atleast one real solution is:

• A. $4$
• B. $6$
• C. $8$
• D. $10$

Answer 1

The correct option is D $10$

Given equation $\Rightarrow 9a^x+\frac{4}{a^x}=\lambda +2$
By AM $\ge$ GM, we have LHS $\ge 12$
$\therefore$ For real solution $\lambda +2\ge 12\Rightarrow \lambda \ge 10$