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Number of solutions of the equation \( \Large \sqrt{x^{2}-x+1}+\frac{1}{\sqrt{x^{2}-x+1}}=2-x^{2} \) is

A) 0
B) 1
C) 2
D) 4

Correct Answer:


B) 1

Description for Correct answer:

We know that, \( \Large AM \ge GM \)

\( \Large \sqrt{a} + \frac{1}{\sqrt{a}} \ge 2 \)

\( \Large \sqrt{x^{2} - x + 1} + \frac{1}{\sqrt{x^{2} - x + 1}} \ge 2 \)

\( \Large 2 - x^{2} \ge 2 \)

\( \Large x^{2} \le 0 \)

=> x = 0

Part of solved Quadratic Equations questions and answers : >> Elementary Mathematics >> Quadratic Equations

Comments

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