If a + b + c = 1, ab + bc = ca = -1 and abc = -1, then what is the value of $a^3 + b^3 + c^3 $?
Answer & explanation
Correct answer: option 4
If a + b + c = 1,
ab + bc = ca = -1
abc = -1
Then what is the value of $a^3 + b^3 + c^3 $?
We know that,
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ac)
(1)2 = a2 + b2 + c2 + 2(-1)
a2 + b2 + c2 = 3
We also know that,
a3 + b3 + c3 - 3abc = ( a + b + c ) ( a2 + b2 + c2 - (ab + bc + ca))
a3 + b3 + c3 - 3(-1) = ( 1 ) ( 3- (-1))
a3 + b3 + c3 = 4 - 3 = 1