SSC CHSL 2025 · PYQ · Algebra · medium
If x + y = 24 and x² + y² = 360, then find the value of (x⁴ + x²y² + y⁴).
Answer
The correct answer is C: 1,17,936. xy = [(x+y)² − (x²+y²)]/2 = [576−360]/2 = 108. x²+y² = 360, so (x²+y²)² = 129600.
- A.2,15,869
- B.1,24,784
- C.1,17,936✓ Correct
- D.1,25,878
xy = [(x+y)² − (x²+y²)]/2 = [576−360]/2 = 108. x²+y² = 360, so (x²+y²)² = 129600. x⁴+y⁴ = 129600 − 2(xy)² = 129600 − 23328 = 106272. x⁴+x²y²+y⁴ = 106272 + 11664 = 117936.
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