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MCQ

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

#### Options

0

1

2

More than two

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#### Solution

We have 2^{x} + x^{2 }= 2 - `1/(2^x)`

⇒ 2 - x^{2} = 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.

Concept: Quadratic and Linear Equation (Entrance Exam)

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