Question 41

The number of real roots of the equation
$$2 \sin\left(\frac{x^2 + x}{6}\right) = 2^x + 2^{-x}$$ is

Solution

In RHS of the equation,

The min value is attained is 2 when x = 0 ( from A.M-GM inequality)

For the LHS side the max value is 2 when sin term has value of 1. But it can not be obtained when x=0

Hence, there are no real solution for the given equation

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