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SSC CHSL 2022 · PYQ · Algebra · medium

If a + 2b = 27 and a³ + 8b³ = 5427, then find the value of 2ab.

  1. A.172
  2. B.156
  3. C.176✓ Correct
  4. D.149

Explanation

a³+8b³ = (a+2b)(a²−2ab+4b²) = 27×(a²−2ab+4b²) = 5427 → a²−2ab+4b² = 201. Also (a+2b)² = a²+4ab+4b² = 729. Subtracting: 6ab = 729−201 = 528 → ab = 88 → 2ab = 176.
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