JAMIA 2021 — Mathematics PYQ
JAMIA | Mathematics | 2021Minimum value of a^{a^x}+\frac a{a^{a^x}} \mathfrak{a}>\mathcal{O};\mathfrak{a},\mathfrak{x}\in\mathbb{R})
Choose the correct answer:
- A.
2a
(Correct Answer) - B.
2a
2a
Explanation
Solution:
Let the two positive terms be:
A=aax
B=aaxa
According to the AM-GM Inequality for positive numbers A and B:
Substituting the values of A and B:
The term aax cancels out inside the square root:
Condition for Equality:
The minimum value occurs when A=B:
(This x exists for any a > 0, a \neq 1. If a=1, the expression is constant at 2).
Minimum Value:
Explanation
Solution:
Let the two positive terms be:
A=aax
B=aaxa
According to the AM-GM Inequality for positive numbers A and B:
Substituting the values of A and B:
The term aax cancels out inside the square root:
Condition for Equality:
The minimum value occurs when A=B:
(This x exists for any a > 0, a \neq 1. If a=1, the expression is constant at 2).
Minimum Value:

