If $x + y + z = 10, xy + yz + zx =25$ and $xyz = 100$, then what is the value of $(x^3 + y^3 + z^3)?$
Answer & explanation
Correct answer: option 3
Given ,
x + y + z = 10
xy + yz + zx = 25
xyz = 100
We know,
x3 + y3 + z3 – 3xyz = (x + y + z) [(x + y + z)2 – 3 (xy + yz + zx)]
x3 + y3 + z3 – 3 × 100 = 10 [102 – 3 × 25]
x3 + y3 + z3 – 300 = 10 (100 – 75) = 10 × 25 = 250
x3 + y3 + z3 = 250 + 300 = 550