If (a + b + c) = 14, and (a3 + b3 + c3 - 3abc) = 98 then, find the value of (ab + bc + ca).
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 63.
a3 + b3 + c3 - 3abc = (a + b + c)[(a + b + c)2 - 3(ab + bc + ca)]
⇒ 98 = 14 × [(14)2 - 3(ab + bc + ca)]
⇒ 7 = 196 - 3(ab + bc + ca)
⇒ 3(ab + bc + ca) = 196 - 7
⇒ 3(ab + bc + ca) = 189
⇒ ab + bc + ca = 63