Các câu hỏi tương tự
CMR nếu: (x + y - c - d)(a - b - c - d) = (a+b - c - d)(a-b+c+d) thì \(\frac{a+b}{a-b}=\frac{c-d}{c+d}\)
Cho các số hữu tỉ \(x=\frac{a}{b};y=\frac{c}{d};z=\frac{a+c}{b+d}\) (a,b,c,d \(\in\) Z ; b>0 ; d>0)
CMR nếu x<y thì x<z<y
CMR nếu \(\frac{a}{b}=\frac{c}{d}\)thì \(\frac{a}{b}=\frac{c}{d}=\frac{a+c}{b+d}\)
CMR
Nếu \(\frac{a}{b}< \frac{c}{d}\) (b,d>0) thì \(\frac{a}{b}< \frac{a+c}{b+d}< \frac{c}{d}\)
a) CMR: Nếu\(\frac{a}{b}=\frac{c}{d}\)thì\(\frac{a}{b}=\frac{a+c}{b+d}\)
b) Cho\(\frac{a+b}{a-b}=\frac{c+a}{c-a}\). CMR: a2 = bc
Bài 1:Cho a;b;c;d thỏa mãn
(a+b+c+d)(a-b-c+d)=(a-b+c-d)(a+d-c-d)
CMR:a;b;c;d lập được thành tỉ lệ thức
Bài 2:Cho\(\frac{x}{a+2b+c}=\frac{y}{2a+b-c}=\frac{z}{4a-4b+c}\)
CMR:\(\frac{a}{x+2y+z}=\frac{b}{2x+y-c}=\frac{c}{4x-4y+z}\)
Bài 3:Cho\(\frac{1}{c}=\frac{1}{2}\left(\frac{1}{a}+\frac{1}{b}\right)CMR:\frac{a}{b}=\frac{a-c}{c-b}\)
a, Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\)CMR \(\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)
b,Cho\(\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}=x\)Tính x
c,Tìm x,y,z biết:xy+x+2y=17
CMR nếu \(\frac{a}{b}=\frac{c}{d}\)thì \(\left(\frac{a-b}{c-d}\right)^4=\frac{a^4+b^4}{c^4+d^4}\)
Bài 1 : a) CMR : nếu \(\frac{a}{b}=\frac{b}{c}=\frac{c}{a}\)thì \(a=b=c\)
b) CMR : nếu \(\frac{a}{b}=\frac{c}{d}=\frac{p}{q}\)thì \(\frac{ma+nc+ep}{mb+nd+eq}=\frac{a}{b}=\frac{c}{d}=\frac{p}{q}\)