If $ x + \frac{1}{x} = 4 $, then $ x^2 + \frac{1}{x^2} = ? $ | Mathematics MCQ

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If $x + \frac{1}{x} = 4$ , then $x^2 + \frac{1}{x^2} =?$

Correct Answer

📐 MA • Math Algebraic Identity FormulaMathematicsPrevious Year Paper 2024

Option C

Quick Summary:

If $x + \frac{1}{x} = k$ , then $x^2 + \frac{1}{x^2} = k^2 - 2$

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📐MAMath SolutionAlgebraic Identity Formula⏱️ 10 Seconds

📋 Given

$x + \frac{1}{x} = 4$

🔢 Step-by-Step Solution

Squaring Both Sides

$\left(x + \frac{1}{x}\right)^2 = 4^2x^2 + 2 \cdot x \cdot \frac{1}{x} + \frac{1}{x^2} = 16x^2 + 2 + \frac{1}{x^2} = 16$

Expanding using (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2

Isolating $x^2 + \frac{1}{x^2}$

$x^2 + \frac{1}{x^2} = 16 - 2 = 14$

x2+1x2=14x^2 + \frac{1}{x^2} = 14x2+x21​=14

✅

C is correct — 14

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