If a + b + c = 6, a3 + b3 + c3 - 3abc = 342, then what is the value of ab + bc + ca ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. -7
Concept
Identity used
a3 + b3 + c3 - 3abc = ( a + b + c) [ ( a + b + c)2 - 3 (ab + bc + ca)]
Application
a3 + b3 + c3 - 3abc = ( a + b + c) [ ( a + b + c)2 - 3 (ab + bc + ca)]
Putting the values
342 = ( 6 ) [ (6)2 - 3 (ab + bc + ca)]
57 = 36 - 3 (ab + bc + ca)
21 = - 3 (ab + bc + ca)
-7 = (ab + bc + ca)