已知x-y+z=0,求证：y²大于等于4xz

已知x-y+z=0,求证：y²大于等于4xz
已知x-y+z=0,求证：y²大于等于4xz

已知x-y+z=0,求证：y²大于等于4xz
x-y+z=0
则y=x+z
所以
y²-4xz
=(x+z)²-4xz
=x²+2xz+z²-4xz
=x²-2xz+z²
=(x-z)²≥0
所以y²≥4xz

y=x+z,y^2=(x+z)^2=x^2+z^2+2xz>=2xz+2xz=4xz,用到不等式