Number of solution of equation 2cos ({e^x}) = {5^x} + {5^{ - x}} , are

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Trigonometrical Equations

easy

The number of solution of the equation $2\cos ({e^x}) = {5^x} + {5^{ - x}}$, are

A

No solution

B

One solution

C

Two solutions

D

Infinitely many solutions

(IIT-1992)

Solution

(a) We know $\frac{{{5^x} + {5^{ – x}}}}{2} \ge 1$, (using $A.M.$ $ \ge $ $G.M.$)

But since ${\rm{cos}}\,({e^x}) \le 1,$

So, there does not exist any solution.

Standard 11

Mathematics

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