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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