Question : If a3 + b3 = 152 and a + b = 8, then what is the value of ab?
Option 1: 2
Option 2: 11
Option 3: –10
Option 4: 15
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Correct Answer: 15
Solution :
a
3
+ b
3
= 152
a + b = 8
Since (a + b)
3
= a
3
+ b
3
+ 3ab(a + b),
⇒ 8
3
= 152 + 3ab × 8
⇒ 24ab = 512 – 152 = 360
$\therefore$ ab = $\frac{360}{24}$ = 15
Hence, the correct answer is 15.
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