Cho $\frac{a}{b+c}$ + $\frac{b}{c+a}$+ $\frac{c}{a+b}$ = 1 . Chứng minh rằng: $\frac{a^2}{b+c}$ + $\frac{b^2}{c+a}$+ $\frac{c^2}{a+b}$ = 0 Xin mọi ng

0 bình luận về “Cho $\frac{a}{b+c}$ + $\frac{b}{c+a}$+ $\frac{c}{a+b}$ = 1 . Chứng minh rằng: $\frac{a^2}{b+c}$ + $\frac{b^2}{c+a}$+ $\frac{c^2}{a+b}$ = 0 Xin mọi ng”

1. Giải thích các bước giải:

   Ta có:
   $C=\dfrac{a^2}{b+c}+\dfrac{b^2}{c+a}+\dfrac{c^2}{a+b}$
   $\to C+(a+b+c)=(\dfrac{a^2}{b+c}+a)+(\dfrac{b^2}{c+a}+b)+(\dfrac{c^2}{a+b}+c)$
   $\to C+(a+b+c)=\dfrac{a(a+b+c)}{b+c}+\dfrac{b(a+b+c)}{c+a}+\dfrac{c(a+b+c)}{a+b}$
   $\to C+(a+b+c)=(a+b+c)(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b})$
   $\to C+(a+b+c)=(a+b+c)\cdot 1$
   $\to C+(a+b+c)=(a+b+c)$
   $\to C=0$
   $\to \dfrac{a^2}{b+c}+\dfrac{b^2}{c+a}+\dfrac{c^2}{a+b}=0$

   $\to đpcm$

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