Các câu hỏi tương tự
12 tháng 12 2017 lúc 21:39
Cho a, b, c > 0. CMR: M = \(\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}\)\(\notin\)Z.
CMR: Nếu a(y+z)=b(z+x)=c(x+y)\(\left(a\ne b\ne c\ne0\right)\)thì \(\frac{y-z}{a\left(b-c\right)}=\frac{z-x}{b\left(c-a\right)}=\frac{x-y}{c\left(a-b\right)}\)
Cho \(a+b+c=a^2+b^2+c^2=1\) và \(\frac{x}{a}=\frac{y}{b}=\frac{z}{c}\left(a\ne0,b\ne0,c\ne0\right)\)
CMR \(\left(x+y+z\right)^2=x^2+y^2+z^2\)
CMR: Nếu a(y + z) = b(z + x) = c(x + y) \(\left(a\ne b\ne c\ne0\right)\)
Thì \(\frac{y-z}{a\left(b-c\right)}=\frac{z-x}{b\left(c-a\right)}=\frac{x-y}{c\left(a-b\right)}\)
Cho a; b; c; x; y; z và \(x^2-yz\ne0;y^2-xz\ne0;z^2-xy\ne0\) thỏa mãn \(\frac{x^2-yz}{a}=\frac{y^2-xz}{b}=\frac{z^2-xy}{c}\) . CMR \(\frac{a^2-bc}{x}=\frac{b^2-ca}{y}=\frac{c^2-ab}{z}\)
cmr nếu\(a\left(z+y\right)=b\left(z+x\right)=c\left(x+y\right);a\ne b\ne c\ne0\Rightarrow\frac{y-z}{a\left(b-c\right)}=\frac{z-x}{b\left(c-a\right)}=\frac{x-y}{c\left(a-b\right)}\)
Cho \(M=\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}\) với a , b , c > 0 . Chứng minh rằng : \(M\notin Z\) .
\(Cho:\frac{2y+2z-x}{a}=\frac{2z+2x-y}{b}=\frac{2x+2y-z}{c};trongđó:a,b,c,2b+2c-a,2c+2a-b,2a+2b-c\ne0.cmr:\frac{x}{2b+2c-a}=\frac{y}{2c+2a-b}=\frac{z}{2a+2b-c}\)
Biết \(\frac{bz-cy}{a}=\frac{cx-az}{b}=\frac{ay-bx}{c}với\left(a,b,c\ne0\right)\)
CMR \(\frac{x}{a}=\frac{y}{b}=\frac{z}{c}\)