\(\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)^2=2^2\)
\(\Rightarrow\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}+2.\frac{1}{a}.\frac{1}{b}+2.\frac{1}{b}.\frac{1}{c}+2.\frac{1}{a}.\frac{1}{c}=4\)
\(\Rightarrow2+2\left(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ac}\right)=4\)
\(\Rightarrow\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ac}=1\)
\(\Rightarrow\frac{a+b+c}{abc}=1\Rightarrow a+b+c=abc\)
Chúc bạn học tốt.
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Cho : 1/a + 1/b + 1/c = 1/ a^2 + 1/b^2 +
1/c^2 = 2
C/m : a+ b + c = abc
