Question

If x+y+z=15 and x 2 +y 2 +z 2 =75, find the value of x 3 +y 3 +z 3 -3xyz.

Answer 1

(x+y+z+)2=X2+Y2+z2+2(XY+yz+zx)
225=75+2(XY+yz+zx)
225-75=2(XY+yz+zx)
150÷2=XY+yz+zx
75=xy+yz+zx
X3+y3+z3-3xyz=[x+y+z][X2+Y2+z2]-[xy+yz+zx]
=15×[75-75]
=0