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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


Team Careers360 24th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

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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