Question

Solve the following question and mark the best possible option.
How many solutions to the equation 2^x + x² = 2 - 1/2^x exist?

Options

• 0

• 1

• 2

• More than two

Answer 1

We have 2^x + x² = 2 - `1/(2^x)`

⇒ 2 - x² = 2^x + `1/(2^x)` ≥ 2  ...[For nonnegative real numbers AM≥GM]

⇒ 2 – x2 ≥ 2 ⇒ x2 ≤ 0

⇒ x = 0 is the only solution to the given equation. Hence this has only one solution.