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Algebra
Algebraic Identities
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RRB NTPC Graduate Tier 1 2025 Shift-1 📅 09 Jun, 2025

If x - (1/x) = 3, then the value of x4 + (1/x4) is:

A
19
B
196
C
176
D
119
Result Summary
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RRB NTPC Graduate Tier 1
2025 • 09 Jun, 2025 • Shift-1
If x - (1/x) = 3, then the value of x4 + (1/x4) is:
Correct Answer
119
First Squaring Operation: We begin with the foundational equation x - (1/x) = 3. To elevate the powers, we square both sides entirely: (x - 1/x)2 = 32.Applying ......
Ref/Book : RRB NTPC Graduate Tier 1 2025
Ref. Subject Algebra
Chapter -
Ref. Topic Algebraic Identities
Pg. No -
💡 Analysis & Explanation
First Squaring Operation ▼
We begin with the foundational equation x - (1/x) = 3. To elevate the powers, we square both sides entirely: (x - 1/x)2 = 32.
Applying Algebraic Identity ▼
Using the standard expansion formula (a - b)2 = a2 + b2 - 2ab, the equation becomes x2 + (1/x2) - 2(x)(1/x) = 9. The x terms cancel out, leaving x2 + (1/x2) - 2 = 9. Adding 2 to both sides yields x2 + (1/x2) = 11.
Second Squaring Operation ▼
To reach the fourth power, we square the newly derived equation: (x2 + 1/x2)2 = 112. Applying the positive expansion formula (a + b)2 = a2 + b2 + 2ab gives x4 + (1/x4) + 2(x2)(1/x2) = 121.
Final Derivation ▼
The variables cancel again, resulting in x4 + (1/x4) + 2 = 121. Subtracting 2 from the right side gives 119.
Conclusion ▼
The final calculated value is exactly 119.
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