\(\frac{a}{c}=\frac{c}{b}\)
\(\Rightarrow\frac{a}{b}=\frac{c}{c}\)
\(\Rightarrow\frac{a}{b}=\frac{c}{c}=\left(\frac{a}{b}\right)^2=\left(\frac{c}{c}\right)^2=\frac{a^2+c^2}{b^2+c^2}\)
\(\Rightarrow\frac{a}{b}=\frac{a^2+c^2}{b^2+c^2}\left(đpcm\right)\)
1. Cho a,b,c,x,y,z khác 0 thỏa mãn:
\(\frac{7cy-5bz}{x}=\frac{2az-7cx}{y}=\frac{5bx-2ay}{z}\)
CMR: \(\frac{2a}{x}=\frac{5b}{y}=\frac{7c}{z}\)
2.Cho a,b,c,x,y,z khác 0 thỏa mãn: \(\frac{x}{a}=\frac{y}{b}=\frac{z}{c}\)
CMR: \(\frac{x^2+y^2+z^2}{\left(ax+by+cz\right)^2}=\frac{1}{a^2+b^2+c^2}\)
3.Cho a,b,c thỏa mãn \(\frac{a}{2016}=\frac{b}{2017}=\frac{c}{2018}\)
CMR: 4(a-b)(b-c)=(a-c)2
4. Cho a,b,c thỏa mãn:\(\frac{a}{x}=\frac{b}{x+1}=\frac{c}{x+2}\)
CMR: 4(a-b)(b-c)=(a-c)2
5. Cho a,b,c thỏa mãn:
\(\frac{a}{-2017}=\frac{b}{-2016}=\frac{c}{-2015}\)
CMR: 4(a-b)(b-c)=(a-c)2
6. Cho a,b,c khác 0 và \(\frac{b+c+a}{a}=\frac{a+b-c}{b}=\frac{c+a-b}{c}\)
Tính giá trị biểu thức A=\(\frac{\left(a-b\right)\left(c+b\right)\left(c-a\right)}{abc}\)
Cho \(\frac{a}{b}=\frac{b}{c}\)CMR :
a) \(\frac{a^2+b^2}{b^2+c^2}=\frac{a}{c}\)
b) \(\frac{c^2-a^2}{a^2+b^2}=\frac{c-a}{a}\)
Cho\(\frac{a}{c}=\frac{c}{b}\)CMR:\(\frac{b^2-a^2}{a^2+c^2}=\frac{b-a}{a}\)
Cho \(\frac{a}{b}=\frac{c}{b}\). Cmr:
a) \(\frac{a}{b}=\frac{a^2+b^2}{c^2+b^2}\)
b) \(\frac{b-a}{a}=\frac{b^2-a^2}{a^2+c^2}\)
\(cho\frac{a}{c}=\frac{c}{b}\)
\(CMR:\frac{a^2+c^2}{b^2+c^2}=\frac{a}{b}\)
Cho\(\frac{a}{c}=\frac{c}{b}\) . CMR: \(\frac{a^2+c^2}{b^2+c^2}=\frac{a}{b}\)
Cho \(\frac{a}{c}=\frac{c}{b}\),với a,b,c khác 0.CMR:\(\frac{b-a}{a}=\frac{b^2-a^2}{a^2+c^2}\)
Cho \(\frac{a}{c}=\frac{c}{b}\),với a,b,c khác 0.CMR:\(\frac{b-a}{a}=\frac{b^2-a^2}{a^2+c^2}\)
Cho : \(\frac{a}{b}=\frac{c}{d}CMR:\)\(\frac{ab}{cd}=\frac{a^2-b^2}{c^2-d^2}v\text{à}\left(\frac{a+b}{c+d}\right)^2=\frac{a^2+b^2}{c^2+d^2}\)
Cho \(Cho\frac{a}{b}=\frac{b}{c}.CMR:\)
\(\frac{a^2+b^2}{b^2+c^2}=\frac{a}{c}\left(b,c\ne0\right)\)
