Question

Cho 3 số hữu tỉ a,b,c tm \(\dfrac{1}{c}=\dfrac{1}{a}+\dfrac{1}{b}\)

CMR: \(\sqrt{a^2+b^2+c^2}\) là số hữu tỉ

Answer 1

\(\dfrac{1}{c}=\dfrac{1}{a}+\dfrac{1}{b}\Leftrightarrow ab=bc+ac\Leftrightarrow2ab-2bc-2ac=0\\ \Leftrightarrow\sqrt{a^2+b^2+c^2}=\sqrt{a^2+b^2+c^2+2ab-2bc-2ac}\\ =\sqrt{\left(a+b-c\right)^2}=\left|a+b-c\right|\left(dpcm\right)\)

Answer 2

Câu 23:

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