If a + b + c = 7 and a3 + b3 + c3 - 3abc = 175, then what is the value of (ab + bc + ca)?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 8.
a + b + c = 7.
On squaring both sides we get,
⇒ a2 + b2 + c2 + 2(ab + bc + ca) = 49.
Now,
a3 + b3 + c3 - 3abc = (a + b + c)[(a2 + b2 + c2 - (ab + bc + ca)].
175 = 7[a2 + b2 + c2 + 2(ab + bc + ca) - 3(ab + bc + ca)]
175 = 7 × [49 - 3(ab + bc + ca)]
25 = 49 - 3(ab + bc + ca)
3(ab + bc + ca) = 24
ab + bc + ca = 8.