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, a2 + b2 = 82 ab = 9 We know, (a + b)2 = a2 + b2 + 2ab ⇒ (a + b)2 = 82 + 2 × 9 ⇒ (a + b)2 = 100 ⇒ (a + b) = 10 Now, (a + b)3 = a3 + b3 + 3ab(a + b) ⇒ (10)3 = a3 + b3 + 3 × 9 × 10 ⇒ 1000 = a3 + b3 + 270 $\therefore$ a3 + b3 = 1000 – 270 = 730 Hence, the correct answer is 730.
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Question : If a3 + b3 = 217 and a + b = 7, then the value of ab is:
Option 1: – 6
Option 2: – 1
Option 3: 7
Option 4: 6
Question : If a + b + c = 6 and a2 + b2 + c2 = 38, then what is the value of a(b2 + c2) + b(c2 + a2) + c(a2 + b2) + 3abc?
Option 1: 3
Option 2: 6
Option 3: –6
Option 4: –3
Question : If a + b + c = 19, ab + bc + ca = 120, then what is the value of a3 + b3 + c3 – 3abc?
Option 1: 18
Option 2: 23
Option 3: 31
Option 4: 19
Question : If a + b + c = 5 and ab + bc + ca = 7, then the value of a3 + b3 + c3 – 3abc is:
Option 1: 15
Option 2: 20
Option 3: 25
Option 4: 30
Question : If a + b + c = 10 and a2 + b2 + c2 = 48, then the value of ab + bc + ca is _______.
Option 1: 25
Option 2: 26
Option 3: 24
Option 4: 18
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