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\(b^2=ac\Rightarrow\frac{b}{c}=\frac{a}{b}=\frac{2010a}{2010b}=\frac{2011b}{2011c}=\frac{2010a+2011b}{2010b+2011c}\)
\(\Rightarrow\frac{b}{c}.\frac{a}{b}=\left(\frac{2010a+2011b}{2010b+2011c}\right).\left(\frac{2010a+2011b}{2010b+2011c}\right)\)
\(\Rightarrow\frac{a}{c}=\frac{\left(2010a+2011b\right)^2}{\left(2010b+2011c\right)^2}\)
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\(\frac{a}{2b}=\frac{b}{2c}=\frac{c}{2d}=\frac{d}{2a}=\frac{a+b+c+d}{2a+2b+2c+2d}=\frac{a+b+c+d}{2\left(a+b+c+d\right)}=\frac{1}{2}\)
\(\Rightarrow a=\frac{2b}{2}=b\) \(c=\frac{2d}{2}=d\)
\(b=\frac{2c}{2}=c\) \(d=\frac{2a}{2}=a\)
\(\Rightarrow a=b=c=d\)
Ta có: \(A=\frac{2011a-2010b}{c+d}+\frac{2011b-2010c}{a+d}+\frac{2011c-2010d}{a+b}+\frac{2011d-2010a}{b+c}\)
\(=\frac{2011a-2010a}{2a}+\frac{2011a-2010a}{2a}+\frac{2011a-2010a}{2a}+\frac{2011a-2010a}{2a}\)
\(=\frac{4a}{2a}=2\)
A ₫ 2 day ban so yeoung cheing nhe. Cac ban kcho mik nha