\(\frac{a+b}{a-b}=\frac{c+d}{c-d}\)
\(\Rightarrow\frac{a+b}{c+d}=\frac{a-b}{c-d}=\frac{\left(a+b\right)-\left(a-b\right)}{\left(c+d\right)-\left(c-d\right)}=\frac{2b}{2d}=\frac{b}{d}\)
\(\Rightarrow\frac{a+b}{c+d}=\frac{b}{d}=\frac{a+b-b}{c+d-d}=\frac{a}{c}\)
\(\Rightarrow\frac{a}{c}=\frac{b}{d}\)
\(\Rightarrow\frac{a}{b}=\frac{c}{d}\) ( ĐPCM ) .
Cho 0 < a < b < c < d
CMR: \(\frac{a}{b+c+d}+\frac{b}{a+c+d}+\frac{c}{a+b+d}+\frac{d}{a+b+c}< 2\)
Cho \(\frac{a+b}{c+d}=\frac{a-b}{c-d}\)
CMR \(\frac{a}{b}=\frac{c}{d}\)
Cho \(\frac{a}{b}=\frac{c}{d}\left(a,b,c\ne0;a\ne b,c\ne d\right)\).CMR: \(\frac{a}{a-b}=\frac{c}{c-d}\)
Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\) cmr:\(\frac{a^{3k}+b^{3k}+c^{3k}}{b^{3k}+c^{3k}+d^{3k}}=\frac{a^k}{d^k}\)
Cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\). CMR:
a) \(\frac{a}{b}=\frac{a+2c}{b+2d}\)
b) \(\frac{a-b}{b}=\frac{a+c-b-d}{b+d}\)
cmr nếu \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{d}{e}\)
thì \(\frac{a}{e}=\left(\frac{a-b+c-d}{b-c+d-e}\right)^4\)
giúp gấp vs mấy bn:
Tìm a,b,c ϵ Q
a)
\(\frac{a}{b}=\frac{c}{d}\left(ac\ne bd\right)Cm:\frac{a^2+b^2}{c^2+d^2}=\frac{ab}{cd}\)
b)CMR nếu \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\)thì\(\frac{a^3+b^3+c^3}{b^3+c^3+d^3}=\frac{a}{d}\)
cho tỉ lệ thức\(\frac{a}{b}=\frac{c}{d}\)
CMR \(\frac{\left(a+b\right)}{\left(c+d\right)}=\frac{a^2+b^2}{c^2+d^2}\)
Cho \(\frac{a}{b}=\frac{c}{d}.CMR:\)
\(\frac{1111.c-99d}{9999.c-11.d}=\frac{1111.a-99.b}{9999.a-11.b}\)