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Solve the Following Question and Mark the Best Possible Option. How Many Solutions to the Equation 2x + X2 = 2 - 1/2x Exist? - Mathematics

MCQ

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

Options

  • 0

  • 1

  • 2

  • More than two

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Solution

We have 2x + x2 = 2 - `1/(2^x)`

⇒ 2 - x2 = 2x + `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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