Cho $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$.CMR:
$\frac{1}{a^{2015}}+\frac{1}{b^{2015}}+\frac{1}{c^{2015}}=\frac{1}{a^{2015}+b^{2015}+c^{2015}}$
Cho $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$.CMR:
$\frac{1}{a^{2015}}+\frac{1}{b^{2015}}+\frac{1}{c^{2015}}=\frac{1}{a^{2015}+b^{2015}+c^{2015}}$
Cho $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$.CMR:
$\frac{1}{a^{2015}}+\frac{1}{b^{2015}}+\frac{1}{c^{2015}}=\frac{1}{a^{2015}+b^{2015}+c^{2015}}$
Ta có
$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$
$\Rightarrow (a+b+c)(ab+bc+ca)=abc\Leftrightarrow (a+b)(b+c)(c+a)=0$
$\begin{bmatrix} a=-b\\ b=-c\\ c=-a \end{bmatrix}$
Đến đây thay và là ra
$\sqrt{VMF}$
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