Question

cho a, b, c là các số thỏa mãn a+b+c=11 và 1/a+b+1/b+c+1/c+a=13/17

Tính A= a/a+b+b/c+a+c/a+b

Answer 1

Ta có: \(\left(a+b+c\right)\left(\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}\right)=11\cdot\frac{13}{17}\)

\(\Rightarrow\frac{a+b+c}{a+b}+\frac{a+b+c}{b+c}+\frac{a+b+c}{c+a}=\frac{143}{17}\)

\(\Rightarrow\frac{a+b}{a+b}+\frac{c}{a+b}+\frac{a}{b+c}+\frac{b+c}{b+c}+\frac{b}{c+a}+\frac{a+c}{c+a}=\frac{143}{17}\)

\(\Rightarrow1+1+1+\frac{c}{a+b}+\frac{a}{b+c}+\frac{b}{c+a}=\frac{143}{17}\)

\(\Rightarrow A=\frac{143}{17}-3=\frac{92}{17}\)