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Minimum value of for which the equation 9a^{2x}-(+2)a^{x}+4=0

Question

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

4

6

8

10

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Mateo Discussed

Minimum value of

λ

for which the equation

9 a^{2 x} - (λ + 2) a^{x} + 4 = 0

a > 1

has atleast one real solution is:

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

Given equation

\Rightarrow 9 a^{x} + \frac{4}{a ^{x}} = λ + 2

By AM

\geq

GM, we have LHS

\geq 12

∴

For real solution

λ + 2 \geq 12 \Rightarrow λ \geq 10

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Question Text	Minimum value of $λ$ for which the equation $9 a^{2 x} - (λ + 2) a^{x} + 4 = 0$ . $a > 1$ has atleast one real solution is:
Answer Type	Text solution:1
Upvotes	150