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NTPC Graduate Tier 1 2025 Shift-3 📅 05 Jun, 2025

If x - (1/x) = 10, then the value of x³ - (1/x³) is:

A
986
B
1030
C
992
D
1386
Result Summary
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NTPC Graduate Tier 1
2025 • 05 Jun, 2025 • Shift-3
If x - (1/x) = 10, then the value of x³ - (1/x³) is:
Correct Answer
1030
[Algebraic Identity Setup]: The problem requires finding the value of an algebraic expression based on a given linear equation. We use the standard identity: (a......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Quantitative Aptitude
Chapter -
Ref. Topic Algebra
Pg. No -
💡 Analysis & Explanation
[Algebraic Identity Setup] ▼
The problem requires finding the value of an algebraic expression based on a given linear equation. We use the standard identity: (a - b)³ = a³ - b³ - 3ab(a - b).
[Formula Adaptation] ▼
Substituting a = x and b = 1/x, the formula transforms into: (x - 1/x)³ = x³ - 1/x³ - 3(x)(1/x)(x - 1/x). Notice that x and 1/x cancel each other out in the product.
[Variable Substitution] ▼
This simplifies to: (x - 1/x)³ = x³ - 1/x³ - 3(x - 1/x). We are given that x - 1/x = 10.
[Calculation Phase] ▼
Plugging in the value 10, we get: 10³ = x³ - 1/x³ - 3(10). This means 1000 = x³ - 1/x³ - 30.
[Final Resolution] ▼
Rearranging to solve for the target expression: x³ - 1/x³ = 1000 + 30 = 1030.
Conclusion ▼
The correctly evaluated value is 1030.
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