\(\frac{a}{b}=\frac{b}{3c}=\frac{c}{9a}\)
\(\Leftrightarrow\left(\frac{a}{b}\right)^3=\left(\frac{b}{3c}\right)^3=\left(\frac{c}{9a}\right)^3=\left(\frac{a.b.c}{b.3c.c.9a}\right)=\frac{1}{27}=k^3\)
\(\Leftrightarrow k=\left(\frac{1}{27}\div\frac{1}{27}\right)\div3=\frac{1}{3}\)
\(\Leftrightarrow\frac{b}{3c}=\frac{1}{3}\)
Vậy \(\Rightarrow b=c\left(đpcm\right)\)
\(cho\frac{a}{b}=\frac{c}{d}\)chứng minh rằng\(\frac{a}{b}=\frac{2a+3c}{2a-3c}\)
cho \(\frac{a}{b}=\frac{c}{d}\) . Chứng minh rằng \(\frac{3a-c}{3b-d}=\frac{a+3c}{b+3d}\)
1. Chứng minh rằng \(\frac{a}{b}\)= \(\frac{c}{d}\)thì \(\frac{a}{b}\)=\(\frac{a+c}{b+d}\)và \(\frac{a}{b}=\)\(\frac{a-c}{b-c}\)
2. Cho \(\frac{a}{b}=\frac{c}{d}\). Chứng minh \(\frac{2a-3c}{2b-3d}=\frac{2a+3c}{2b+3d}\)
cho tỉ lệ thức \(\frac{a}{b}=\frac{c}{d}\). Chứng minh
a)\(\frac{3a+5b}{3a-5b}=\frac{3c+5d}{3c-5d}\)
b)\(\frac{2a+3b}{2a-3b}=\frac{2c+3d}{2c-3d}\)
Cho \(\frac{a}{b}=\frac{c}{d}\), Chứng minh rằng \(\frac{2a-3c}{2b-3d}=\frac{2a+3c}{2a+3d}\)
Cho \(\frac{a}{b}=\frac{c}{d}\), Chứng minh rằng \(\frac{2a-3c}{2b-3d}=\frac{2a+3c}{2a+3d}\)
cho a,b,c,d>0 chứng minh \(\frac{a}{b+c}+\frac{b}{c+d}+\frac{c}{a+d}+\frac{d}{a+b}\ge2\)
Cho\(\frac{a}{b}=\frac{b}{c}=\frac{c}{a}\)
Chứng minh ràng : a = b = c
Cho \(\frac{a}{b}=\frac{c}{d}\).Hãy chứng minh:
\(\frac{a+c}{b+d}=\frac{a-c}{b-d}\)
