SSC CHSL 2022 · PYQ · Algebra · medium
If x + 1/x = −2√3, what is the value of x⁵ + 1/x⁵?
Answer
The correct answer is A: -182√3. Let s = x+1/x = −2√3. Then x²+1/x² = s²−2 = 12−2=10.
- A.-182√3✓ Correct
- B.182√3
- C.-178√3
- D.-180√3
Let s = x+1/x = −2√3. Then x²+1/x² = s²−2 = 12−2=10. x³+1/x³ = s³−3s = −24√3+6√3 = −18√3. x⁵+1/x⁵ = (x²+1/x²)(x³+1/x³)−(x+1/x) = 10×(−18√3)−(−2√3) = −180√3+2√3 = −178√3. Answer is (a) −178√3.
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