Áp dụng tính chất của dãy tỉ số bằng nhau
\(\frac{a+b+c}{a+b-c}=\frac{a-b+c}{a-b-c}=\frac{a+b+c-\left(a-b+c\right)}{a+b-c-\left(a-b-c\right)}=\frac{a+b+c-a+b-c}{a+b-c-a+b+c}=1\)
\(\Rightarrow\frac{a+b+c}{a+b-c}=1\Rightarrow a+b+c=a+b-c\Rightarrow2c=0\Rightarrow c=0\)
Chon cau tra loi dung Neu a+b/b+c=c+d/d+a thi
a)a phai bang c
b)a=c hay a+b+c+d=0
c)a+b+c+d phai bang 0
d)a+b+c+d khac 0 neu a=c
Cho 1/c=1/2(1/a+1/b)(voi a,b,ckhac 0; b khac c). CMRa/b=a-c/c-b
cho a,b,c khac 0 ; a++b+c khac 0 thoa man \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}\)
CMR\(\frac{1}{a^{2009}}+\frac{1}{b^{2009}}+\frac{1}{c^{2009}}=\frac{1}{a^{2009}+b^{2009}+c^{2009}}\)
cmr
a+b/c+d=b+c/d+a trong do a+b+c+d khac 0 thi a=c
biet x=\(\frac{a}{b+c}\)=\(\frac{b}{c+a}\)=\(\frac{c}{a+b}\)
tim x trong 2 truong hop sau
a] a+b+c=0
b] a+b+c khac 0
chun to ran neu \(\frac{a}{b}\)<\(\frac{c}{d}\)(b.0,d>0) thi \(\frac{a}{b}\)<\(\frac{a+c}{b+d}\)<\(\frac{c}{d}\)
P=\(\frac{2a-b}{c+d}\)+\(\frac{2b-c}{d+a}\)+\(\frac{2c-d}{a+b}\)+\(\frac{2d-a}{b+c}\)
Tinh P biet :
\(\frac{a}{b}\)=\(\frac{b}{c}\)=\(\frac{c}{d}\)=\(\frac{d}{a}\)
trong do ( a+b+c+d ) khac 0
cho a,b,c khac 0 va\(\frac{a+b-c}{c}=\frac{b+c-a}{a}=\frac{c+a-b}{b}\)
Tính \(P=\left(1+\frac{b}{a}\right)\left(1+\frac{c}{b}\right)\left(1+\frac{a}{c}\right)\)
cho a,b,c khac 0 thoa man\(\frac{a+b+c}{c}=\frac{a-b+c}{b}=\frac{-a+b+c}{a}\)
tinh m=\(\frac{\left(a+b\right)\cdot\left(b+c\right)\cdot\left(c+a\right)}{a\cdot b\cdot c}\)
