Question : If a2 + b2 = 82 and ab = 9, then a possible value of a3 + b3 is:
Option 1: 720
Option 2: 750
Option 3: 830
Option 4: 730
Correct Answer: 730
Solution : Given, a 2 + b 2 = 82 ab = 9 We know, (a + b) 2 = a 2 + b 2 + 2ab ⇒ (a + b) 2 = 82 + 2 × 9 ⇒ (a + b) 2 = 100 ⇒ (a + b) = 10 Now, (a + b) 3 = a 3 + b 3 + 3ab(a + b) ⇒ (10) 3 = a 3 + b 3 + 3 × 9 × 10 ⇒ 1000 = a 3 + b 3 + 270 $\therefore$ a 3 + b 3 = 1000 – 270 = 730 Hence, the correct answer is 730.
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