Question

calculati xyz daca x^3+y^3+z^3=x^2+y^2+z^2=x+y+z=1

Answer 1

x+y+z=1 =>
(x+y+z)²=x²+y²+z²+2(xy+xz+yz) =>
xy+xz+yz=0
folosind identitatea
x³+y³+z³  -  xyz= (x+y+z)(x²+y²+z²-xy-xz-yz)  =>
1 - xyz= 1(1-0) =>
1 - xyz =1 =>
xyz=0
sa cresti mare :D