If a + b + c = 7 and a3 + b3 + c3 - 3abc = 175, then what is the value of ab + bc + ca?
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 8.
a3 + b3 + c3 - 3abc = (a + b + c)3 - 3(a + b + c)(ab + bc + ca)
⇒ 175 = (7)3 - 3 × 7 × (ab + bc + ca)
⇒ 175 = 343 - 21(ab + bc + ca)
⇒ 21(ab + bc + ca) = 168
⇒ (ab + bc + ca) = 8