If a − b = 4 and a³ − b³ = 88, then find the value of a² − b².
A.7√6
B.9√6
C.8√6✓ Correct
D.6√6
Explanation
a³−b³ = (a−b)(a²+ab+b²) = 88, so a²+ab+b²=22. Also (a−b)²=a²−2ab+b²=16, giving a²+b²=16+2ab. So 16+2ab+ab=22 → 3ab=6 → ab=2. Then a²+b²=16+4=20, so (a+b)²=20+4=24, a+b=2√6. Thus a²−b²=(a+b)(a−b)=2√6×4=8√6.
💡 Practice unlimited SSC CHSL PYQs + AI-tracked progress on each topic. Sign up free →