If x+y+z = 2, xy+yz+zx = -11 , and xyz = -12, then what is the value of x3 + y3 + z3?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 38
Concept Used :
x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx). .....(i)
Given :
1. x + y + z = 2
2. xy + yz + zx = -11
3. xyz = -12
Solution :
(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
From the given values
(2)2 = x2 + y2 + z2 + 2(-11)
x2 + y2 + z2 = 22 + 4 = 26 ......(ii)
Now, putting the given values in equation (i)
x3 + y3 + z3 – 3(-12) = (2)(26 + 11)
x3 + y3 + z3 = 74 - 36 = 38
The required value = x3 + y3 + z3 = 38.