Question

# The number of real solutions of the equation $$\sin(\mathrm{e}^{\mathrm{x}})=5^{\mathrm{x}}+5^{-x}$$ is (are)

A
0
B
1
C
2
D
Infinitely many

Solution

## The correct option is A $$0$$$$\sin (e^{x})$$ has a max value of 1.$$5^{x}+5^{-x}$$ has a max value of 2.$$A.M\geq G.M$$$$\Rightarrow \dfrac{5^{x}+5^{-x}}{2}\geq \sqrt{5^{x}.5^{-x}}$$$$5^{x}+5^{-x}\geq 2.$$$$\therefore$$ There is no point of intersection of both.$$\therefore$$ No solution.Mathematics

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