Question

Pls solve both the questions and dont ignore...​

Answer 1

Answer:

x+y+z=8

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

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

Substituting the values for (x+y+z)= 8,(xy+yz+zx)=20

We have

8^2=x^2+y^2+z^2+2(20)  

64=x^2+y^2+z^2+2(20)  

64-40=x^2+y^2+z^2

24=x^2+y^2+z^2

x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx).

=8*(24-20)

=8*4

=32

ii)x+y+z=15

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

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

Substituting the values for (x+y+z)= 15,x^2+y^2+z^2=33

We have

15^2=33+2(xy+yz+zx)  

225=33+2(xy+yz+zx)  

225-33=2(xy+yz+zx)

192/2=xy+yz+zx

96=xy+yz+zx

x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx).

=15*(33-96)

=15*-63

=-945