数学题啊啊啊啊啊啊啊

实数X,Y,Z满足x*y*z=1,求证X^2+Y^2+Z^2+3>=2(XY+YZ+ZX)

若x,y,z是正数，且xy+yz+xz=1，求证8x^2y^2z^2≥（1-x^2)(1-y^2)(1-z^2)

设证实数x，y满足x^3+y^3=x-y,求证x^2+4y^2<1

求各位大小牛帮忙！！！！

（x+1)^2+（y+1)^2+（z+1)^2≥0

x^2+2x+1+y^2+2y+1+z^2+2z+1≥0

X^2+Y^2+Z^2+3>=2(XY+YZ+ZX)

x*y*z=1

X^2+Y^2+Z^2>=3(3)√X^2 x Y^2 x Z^2=3

XY+YZ+ZX>=3(3)√XY x YZ x ZX =3

so X^2+Y^2+Z^2+3>=2(XY+YZ+ZX)