已知x-y+z=0,求证:y²大于等于4xz
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/12 19:23:58
![已知x-y+z=0,求证:y²大于等于4xz](/uploads/image/z/14307356-20-6.jpg?t=%E5%B7%B2%E7%9F%A5x-y%2Bz%3D0%2C%E6%B1%82%E8%AF%81%EF%BC%9Ay%26%23178%3B%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E4xz)
x){}K+t+l
tmlzYjʆO,N iRQeTO;rl1ҶB"`&T.LP&`D@ۨJ
.$(]Q: Y] 1M0V8#{tEvmYĶ@:ϧxڱɎ^G2
p
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