Theo t/c dãy tỉ số bằng nhau:
\(\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}=\frac{a+b+c}{b+c+c+a+a+b}=\frac{a+b+c}{2.\left(a+b+c\right)}=\frac{1}{2}\)
=> \(2a=b+c\)
=> \(2b=c+a\)
=> \(2c=a+b\)
Do đó:
\(A=2a+2b+2c=b+c+c+a+a+b=2.\left(a+b+c\right)\)
Cho \(\frac{2a+b}{c}=\frac{2b+c}{a}=\frac{2c+a}{b}.Tính: \frac{2a+b}{c}+\frac{a}{2b+c}+\frac{3b}{2c+a}\)
CHO \(\frac{2a+b}{c}=\frac{2b+c}{a}=\frac{2c+a}{b}\)
TíNH.\(\frac{2a+b}{c}+\frac{a}{2b+c}+\frac{3b}{2c+a}\)
cho a,b,c khác 0 và \(\frac{2a+b}{c}=\frac{2b+c}{a}=\frac{2c+a}{b}\)
Tính \(P=\frac{2a+b}{c}+\frac{2b+c}{a}+\frac{3b}{2c+a}\)
\(Cho:\frac{2y+2z-x}{a}=\frac{2z+2x-y}{b}=\frac{2x+2y-z}{c};trongđó:a,b,c,2b+2c-a,2c+2a-b,2a+2b-c\ne0.cmr:\frac{x}{2b+2c-a}=\frac{y}{2c+2a-b}=\frac{z}{2a+2b-c}\)
Cho:\(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{d}{a}\)
Tính: P\(\frac{2a-b}{2c-d}+\frac{2b-c}{2d-a}+\frac{2c-d}{2a-b}+\frac{2d-a}{2b-c}\)
Giúp với ai nhanh mình tick cho.
TÍnh giá trị của biểu thức :
A = \(\frac{2a+b}{c}\)+ \(\frac{a}{2b+c}\)+\(\frac{3b}{2c+a}\) biết \(\frac{2a+b}{c}\)=\(\frac{2b+c}{a}\)=\(\frac{2c+a}{b}\)
cho \(\frac{a}{b+2c}=\frac{b}{c+2a}=\frac{c}{a+2b}\)
tính giá trị M=\(\frac{a}{b+2c}\cdot\frac{b}{c+2a}\cdot\frac{c}{a+2b}\)
Cho a,b,c>0 và \(\frac{2b+c-a}{a}=\frac{2c-b+a}{b}=\frac{2a+b-c}{c}\). Tính \(P=\frac{\left(3a-2b\right)\left(3b-2c\right)\left(3c-2a\right)}{\left(3a-c\right)\left(3b-a\right)\left(3c-b\right)}\)
Cho \(\frac{a+2c}{b+2d}=\frac{2a+c}{2b+d}\) .
CMR : \(\frac{a}{b}=\frac{a+c}{b+d};\frac{2a-c}{2b-d}=\frac{a-2c}{b-2d};\frac{a+2b}{a-b}=\frac{c+2d}{c-d}\)
