Multiple choice

$Given, (A + B = 11) and (A^2 + B^2 = 65) Quantity I: (A^3 + B^3) Quantity II: (21^2)$

  1. Q1 > Q2

  2. Q1 = Q2

  3. Q1 < Q2

  4. Relationship cannot be established

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From A+B=11, we can find AB. Using (A+B)² = A²+B²+2AB, we get 121 = 65+2AB, so 2AB=56 and AB=28. Now A³+B³ = (A+B)(A²-AB+B²) = 11 × (65-28) = 11×37 = 407. Quantity II is 21² = 441. Since 407 < 441, Q1 < Q2. The correct answer is C.

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