Question

Cho a+b+c=2007 và 1/a+b + 1/b+c + 1/c+a = 90 . Tính M = a/b+c + b/a+c + c/a+b

Answer 1

Lời giải:

$(a+b+c)(\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a})=2007.90$

$\Rightarrow \frac{a}{a+b}+\frac{a}{b+c}+\frac{a}{c+a}+\frac{b}{a+b}+\frac{b}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}+\frac{c}{b+c}+\frac{c}{c+a}=180630$

$\Rightarrow \frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}+\frac{a+b}{a+b}+\frac{b+c}{b+c}+\frac{c+a}{c+a}=180630$

$\Rightarrow M+1+1+1=180630$

$\Rightarrow M =180627$