CAT 2020 Functions Question (Medium)

Question

The number of real-valued solutions of the equation is

Accepted Answer

Step-wise solution 1. Rewrite the equation as . 2. For any real , by AM GM on , with equality only at . 3. Since , , with equality only at . 4. Thus LHS and RHS . For the equality to hold, both must equal simultaneously, which would require and at the same time impossible. 5. Therefore, there are no

CAT 2020

Quantitative

Functions

Medium

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

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