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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