Question

a + b + c =1 ; 1/a + 1/b +1/c = 0 CMR a^2 + b^2 +c^2 =1

Answer 1

Ta có :

\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\)

\(\Rightarrow\frac{bc}{abc}+\frac{ac}{abc}+\frac{ab}{abc}=0\)

\(\Rightarrow\frac{bc+ac+ab}{abc}=0\)

\(\Rightarrow bc+ac+ab=0\)

Lại có :

\(\left(a+b+c\right)^2=1^2\)

\(a^2+b^2+c^2+2\left(ab+bc+ca\right)=1\)

Mà \(bc+ac+ab=0\)(cmt)

\(\Rightarrow a^2+b^2+c^2=1\)

Vậy ...

Answer 2

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