Ta có \(x+y+z=0\)
\(\Rightarrow y+z=-x\)
\(\Rightarrow\left(y+z\right)^2=x^2\)
\(\Rightarrow y^2+z^2-x^2=-2yz\)
Chứng minh tương tự ta có : \(x^2+y^2-z^2=-2xy;x^2+z^2-y^2=-2zx\)
\(\Rightarrow M=\frac{-1}{2yz}+\frac{-1}{2xy}+\frac{-1}{2xz}=\frac{-x-y-z}{2xyz}\)
cái này mình không chắc nha
cho x,y,z đôi một khac nhau va 1/x +1/y+1/z=0 .tinh gia tri bieu thuc A=(x.y/x2+2yz)+(xz/y2+2xz)+(xy/z2+2xy)
Cho x,y,z la 3 so khac 0 va x+y+z=0. Tinh gia tri bieu thuc:
(xy/x^2+y^2-z^2) + ( xz/x^2+z^2-yy^2) + (yz/y^2+z^2-x^2)
tim gia tri nho nhat cua bieu thuc P=1/x^2+x+1/y^2+y+1/z^2+z
cho x+y+z=1, x2+y2+z2=1, x3+y3+z3=1
Tinh gia tri bieu thuc: P = x2007+ y2007+ z2007
cho:1/x2+1/y2+1/z2=2;x+y+z=2xyz;x;y;z khac 0 tinh gia tri bt
\(m=\frac{x^2+y^2}{\left(x+z\right)\left(y+z\right)}+\frac{y^2+z^2}{\left(x+y\right)\left(x+z\right)}+\frac{x^2+z^2}{\left(x+y\right)\left(y+z\right)}\)
Cho x,y,z la cac so nguyen duong thoa man 1/x + 1/y + 1/z = 2015.
Tim GTLN cua bieu thuc P=x+y/x^2+y^2 + y+z/y^2+z^2 + z+x/z^2+x^2
cho x+y =1 . tinh gia tri cua bieu thuc A=x^3+y^3+3xy
chox-y=1. tinh gia tri cua bieu thuc B=x^3-y^3-3xy
cho x+y=1 . tinh gia tri cua bieu thuc C=x^3+y^3+3xy(x^2+y^2)+6x^2*y^2(x+y)
CMR neu x,y,z la 3 so phan biet thi M co gia tri la so ngyen M=x^2/(x-y)(x-z) + y^2/(y-z)(y-x) + z^2/(z-x)(z-y)
chung minh rang bieu thuc 4x(x+y)(x+y+z)(x+y) y^2x^2 luon luon khong am voi moi gia tri cua x,y va z
