giả sử các tỷ lệ đã cho hoặc yêu cầu đều có nghĩa.
Cho tỷ lệ thức: \(\frac{a}{b}\)=\(\frac{c}{d}\)
CMR: a, \(\frac{a}{b}\)=\(\frac{a+2c}{b+2d}\) b, \(\frac{a-b}{b}\)=\(\frac{a+c-b-d}{b+d}\) c,\(\frac{a^3+2c^3}{b^3+d^3}\)=\(\frac{\left(a+c\right)^3}{\left(b+d\right)^3}\) d,\(\frac{ab}{cd}\)=\(\frac{\left(a+2b\right)^2}{\left(c+2d\right)^2}\)
bài 1: cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\)
a) CMR: (a+2c)(b+d)=(a+c)(b+2d) \(\left(b,d\ne0\right)\)
b) CMR: (a+c)(b-d)=ab-cd
c) CMR: \(\frac{a}{a-b}=\frac{c}{c-d}\left(a,b,c,d>0;a\ne b,c\ne d\right)\)
bài 2: cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}CMR:\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{d}\)
Cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\left(b\ne d\right)\).Chứng tỏ rằng ta có các tỉ lệ thức:
\(\frac{ab}{cd}=\frac{\left(a-2b\right)^2}{\left(c-2d\right)^2}\)
Cho tỉ lệ thức :\(\frac{a}{b}=\frac{c}{d}\)
CMR : \(\left(a+2c\right).\left(b+d\right)=\left(a+c\right).\left(b+2d\right)\)
Cho \(\frac{a}{b}=\frac{c}{d}\). Chứng minh:
a) \(\frac{\left(a-b\right)^3}{\left(c-d\right)^3}=\frac{3a^2+2b^2}{3c^2+2d^2}\)
b)\(\frac{4a^4+5b^4}{4c^4+5d^4}=\frac{a^2b^2}{c^2d^2}\)
c)\(\left(\frac{a-b}{c-d}\right)^{2005}=\frac{2a^{2005}-b^{2005}}{2c^{2005}-d^{2005}}\)
d)\(\frac{2a^{2005}+5b^{2005}}{2c^{2005}+5d^{2005}}=\frac{\left(a+b\right)^{2005}}{\left(c+d\right)^{2005}}\)
e)\(\frac{\left(20a^{2006}+11b^{2006}\right)^{2007}}{\left(20a^{2007}-11b^{2007}\right)^{2006}}=\frac{\left(20c^{2006}+11d^{2006}\right)^{2007}}{\left(20c^{2007}-11d^{2007}\right)^{2006}}\)
f)\(\frac{\left(20a^{2007}-11c^{2007}\right)^{2006}}{\left(20a^{2006}+11c^{2006}\right)^{2007}}=\frac{\left(20b^{2007}-11d^{2007}\right)^{2006}}{\left(20b^{2006}+11d^{2006}\right)^{2007}}\)
cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\)CM
a)\(\frac{a\cdot c}{b\cdot d}=\frac{a^2+c^2}{b^2+d^2}\)
b)\(\frac{ab}{cd}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
c)\(\left(a+2c\right)\cdot\left(b+d\right)=\left(a+c\right)\cdot\left(b+2d\right)\)
giúp mk vs
Cho \(\frac{a}{b}=\frac{c}{d}\)CMR:
a,\(\frac{2a^2-3b^2}{2c^2-3d^2}=\frac{ab}{cd}\)
b,\(\frac{ab}{cd}=\frac{\left(a-2b\right)^2}{\left(c-2d\right)^2}\)
Cho tỉ lệ thức : \(\frac{a}{b}=\frac{c}{d}\)
Chứng minh: \(\left(a+2c\right).\left(b+d\right)=\left(a+c\right).\left(b+2d\right)\)
Cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\), Chứng Minh rằng:
\(\frac{\left(a-b\right)^3}{\left(c-d\right)^3}=\frac{3a^2+2b^2}{3c^2+2d^2}\)
M.N giải giúp mk, ai đúng mk chọn
cho \(\frac{a}{b}\)=\(\frac{c}{d}\) CMR
A)\(\frac{3a-2c}{3b+2d}\)= \(\frac{2a+5c}{2b+5d}\)
B)\(\frac{a^3}{b^3}\) =\(\frac{\left(a+c\right)^3}{\left(b+d\right)^5}\)
