Question

Cho a,b,c thỏa mãn: a + b + c = 0. Chứng minh rằng:

   ab + bc + ca \(< =\)0

Answer 1

Ta có : \(\left(a+b+c\right)^2=a^2+b^2+c^2+2\left(ab+bc+ac\right)=0\)

\(\Leftrightarrow a^2+b^2+c^2=-2\left(ab+bc+ac\right)\)

\(\Rightarrow ab+bc+ac=-\frac{1}{2}\left(a^2+b^2+c^2\right)\)

Vì \(a^2+b^2+c^2\ge0\)  \(\forall a;b;c\)

\(\Rightarrow-\frac{1}{2}\left(a^2+b^2+c^2\right)\le0\)  \(\forall a;b;c\)

Hay \(ab+bc+ac\le0\) (đpcm)

Answer 2

ab + bc + ca<= 0  thì a10 +b10 + c10+(b+c+a)

Answer 3

ab + bc + ac \(\le\)0 (đpcm)

  Ủng hộ tớ đi!