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NTPC Graduate Tier 1 2025 Shift-2 📅 05 Jun, 2025

If x + (1/x) = 3, then evaluate the value of x² + (1/x²).

A
7
B
9
C
6
D
11
Result Summary
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NTPC Graduate Tier 1
2025 • 05 Jun, 2025 • Shift-2
If x + (1/x) = 3, then evaluate the value of x² + (1/x²).
Correct Answer
7
Mathematical Premise: The problem presents a base linear algebraic equation: x + 1/x = 3. We must elevate this to a quadratic state.Squaring Protocol: Square bo......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Algebra
Pg. No -
💡 Analysis & Explanation
Mathematical Premise ▼
The problem presents a base linear algebraic equation: x + 1/x = 3. We must elevate this to a quadratic state.
Squaring Protocol ▼
Square both entire sides of the given equation to maintain mathematical equivalence. This produces (x + 1/x)² = 3².
Identity Expansion ▼
Apply the standard algebraic identity (a + b)² = a² + b² + 2ab. Our equation unfolds as x² + (1/x)² + 2(x)(1/x) = 9.
Term Cancellation ▼
In the middle term, the 'x' entirely cancels out the '(1/x)', leaving strictly x² + 1/x² + 2 = 9.
Conclusion ▼
By isolating the target variable, x² + 1/x² logically equates to 9 - 2, finalizing firmly at 7.
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