Question

If x+y+z=12 and x²+y²+ z²=70 then find the value of x³+y³+z³

Answer 1

Answer:

Step-by-step explanation:

(x+y+z)^2= x ^2 + y^2 + z^2 +2xy+2yz+2zx

12^2= 70+2(xy+yz+zx)

2(xy+yz+zx)=144-70

xy+yz+zx=74/2

xy+yz+zx=37

now,

x^3 + y^3 + z^3 - 3xyz = (x+y+z)( x^2 + y^2 + z^2 -xy-yz-zx)

                                      = (12)(70-37)

                                       =(12)(33)

                                        =396