cho a,b,c khac 0 thoa man a^b=b^c=c^a
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Tim a,b,c thoa man khac 0 thoa man:
a+b-2/c= b+c+1/a= c+a+1/b= a+b+c/ 2
cho a , b ,c khac 0 thoa man a + b + c = 0 tinh A = (1+a/b)(1+b/c)(1+c/a)
tim 3 so a,b,c khac nhau va khac 0 thoa man : a/(b+c) = b/(a+c) = c/(a+b)
Cho 3 so a,b,c khac 0 va doi mot khac nhau thoa man a^2.(b+c)=b^2.(a+c)=2015 Tinh c^2.(a+b)
cho 3 so a,b,c khac thuoc Q khac nhau tung doi mot va khac 0 thoa man a/b+c=b/a+c=c/a+b
Chung minh b+c/a+a+c/b+a+b/c khong phu thuoc vao cac gia tri cua a,b,c
Cho a b c khac 0 thoa man a/1=b/2=c/3.
CMR (a+b+c).(1/a+4/b+9/c)=36
cho cac so thuc a, b,c khac 0 thoa man a^2*(a+b)=b^2*(b+c)=2016. tinh bieu thuc A=c^2*(a+c)
cho a,b,c khac 0 thoa man ab/a+b=bc/b+c=ca/c+a tinh M=ab+bc+ca/a^2+b^2+c^2
Từ \(\dfrac{ab}{a+b}=\dfrac{bc}{b+c}=\dfrac{ca}{c+a}\)
\(\Rightarrow\dfrac{a+b}{ab}=\dfrac{b+c}{bc}=\dfrac{c+a}{ca}\)
\(\Rightarrow\dfrac{a}{ab}+\dfrac{b}{ab}=\dfrac{b}{bc}+\dfrac{c}{bc}=\dfrac{c}{ca}+\dfrac{a}{ca}\)
\(\Rightarrow\dfrac{1}{b}+\dfrac{1}{a}=\dfrac{1}{c}+\dfrac{1}{b}=\dfrac{1}{a}+\dfrac{1}{c}\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{1}{b}+\dfrac{1}{a}=\dfrac{1}{c}+\dfrac{1}{b}\\\dfrac{1}{c}+\dfrac{1}{b}=\dfrac{1}{a}+\dfrac{1}{c}\\\dfrac{1}{a}+\dfrac{1}{c}=\dfrac{1}{b}+\dfrac{1}{a}\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}\dfrac{1}{a}=\dfrac{1}{c}\\\dfrac{1}{b}=\dfrac{1}{a}\\\dfrac{1}{c}=\dfrac{1}{b}\end{matrix}\right.\)
\(\Rightarrow\dfrac{1}{a}=\dfrac{1}{b}=\dfrac{1}{c}\Rightarrow a=b=c\)
Khi đó: \(M=\dfrac{ab+bc+ca}{a^2+b^2+c^2}=\dfrac{1\cdot1+1\cdot1+1\cdot1}{1^2+1^2+1^2}=\dfrac{3}{3}=1\)
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Tim cac so a, b, c khac 0 thoa man: a + b - 2 / c = b + c +1 / a = c + a +1 / b = a + b +c / 2