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 : a3 + b3 = 152 a + b = 8 Since (a + b)3 = a3 + b3 + 3ab(a + b), ⇒ 83 = 152 + 3ab × 8 ⇒ 24ab = 512 – 152 = 360 $\therefore$ ab = $\frac{360}{24}$ = 15 Hence, the correct answer is 15.
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Question : If (a – b) = 1, what is the value of (a3 – b3)?
Option 1: a2 + ab + b2
Option 2: (a + b)2 + 3ab
Option 3: a2 – ab + b2
Option 4: a2 + 2ab + b2
Question : If (a – b) = 1 and ab = 6, then what is the value of (a3 – b3)?
Option 1: 21
Option 2: 23
Option 3: 19
Option 4: 25
Question : If a + b + c = 1, ab + bc + ca = –22 and abc = –40, then what is the value of a3 + b3 + c3 ?
Option 1: 67
Option 2: –53
Option 3: –51
Option 4: 27
Question : If a + b = 8, ab = 10, then the value of a3 + b3 is:
Option 1: 312
Option 2: 215
Option 3: 272
Option 4: 111
Question : What is the possible value of (a + b + c) – 3, if a2 + b2 + c2 = 9 and ab + bc + ca = 8?
Option 1: 5
Option 2: 3
Option 3: 9
Option 4: 2
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