The number of real-valued solutions of the equation $$2^{x}+2^{-x}=2-(x-2)^{2}$$ is:

Question

Accepted Answer

0. The graphs of 2 x + 2 − x a n d 2 − ( x − 2 ) 2 2^{x}+2^{-x} and 2-(x-2)^{2} 2 x + 2 − x an d 2 − ( x − 2 ) 2 never intersect. So, number of solutions=0. Alternate method: We notice that the minimum value of the term in the LHS will be greater than or equal to 2 {at x=0; LHS = 2}. However, the term

The number of real-valued solutions of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ is:

The number of real-valued solutions of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ is:

The number of real-valued solutions of the equation 2x+2−x=2−(x−2)22^{x}+2^{-x}=2-(x-2)^{2}2x+2−x=2−(x−2)2 is:

The number of real-valued solutions of the equation 2x+2−x=2−(x−2)22^{x}+2^{-x}=2-(x-2)^{2}2x+2−x=2−(x−2)2 is:

The number of real-valued solutions of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ is:

The number of real-valued solutions of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ is: