No. of real solutions of the equation $2 \cos (\frac{x^2 + x}{6}) = 2^x + 2^{-x} $ How many real solutions are there of the equation $2 \cos (\frac{x^2 + x}{6}) = 2^x + 2^{-x} $?
Please illustrate.

AM-GM inequality says: $2^x + 2^{-x} \geq 2 \geq 2cos\left(\dfrac{x^2 + x}{6}\right)$. so equation occurs when: $2^x = 2^{-x}$ or $x = 0$, and this is the solution of the equation.
