\(a+b+c=0\Rightarrow a^2+b^2+c^2+2\left(ab+bc+ca\right)=0\)
\(\Rightarrow a^2+b^2+c^2=-2\left(ab+bc+ca\right)\)
\(\Rightarrow\left(a^2+b^2+c^2\right)^2=4\left(ab+bc+ca\right)^2\)
\(\Rightarrow a^4+b^4+c^4+2a^2b^2+2b^2c^2+2c^2a^2=4\left(a^2b^2+b^2c^2+c^2a^2+2abc\left(a+b+c\right)\right)\)
\(\Rightarrow a^4+b^4+c^4=2\left(a^2b^2+b^2c^2+c^2a^2\right)\)
\(\Rightarrow2\left(a^4+b^4+c^4\right)=\left(a^2+b^2+c^2\right)^2\)
Vậy ta có đpcm
Cho ba số a,b,c thỏa mãn a+b+c=0.CMR (a^2 +b^2 +c^2)^2 =2(a^4 +b^4 +c^4)
cho a+b+c=0 cmr : a^4+b^4+c^4=1/2. (a^2+b^2+c^2)^2
Cho hai số thực a, b, c thỏa mãn a+b+c=0 cmr a^4+b^4+c^4= 1/2(a^2+b^2+c^2)^2
Cho các số thực a, b, c thỏa mãn a+b+c=0.cmr a^4+b^4+c^4= 1/2(a^2+b^2+c^2)^2
Cho a+b+c=0 CMR
1. a^4 + b^4 + c^4 = 2( a^2b^2 + b^2c^2 + c^2a^2 )
2. a^4 + b^4 + c^4 = 2( ab + bc + ca )^2
3. a^4 + b^4 + c^4 = (a^2 + b^2 + c^2)^2 /2
Cho a, b, c >0. Cmr: a/(b+c)^2 +b/(a+c)^2 +c/(a+b)^2 >=9/4(a+b+c)
Cho a+b+c=0 CMR:\(\left(a^2+b^2+c^2\right)^2=2\left(a^4+b^4+c^4\right)\)
cho a + b +c =0. CMR : \(a^4+b^4+c^4=\frac{1}{2}\left(a^2+b^2+c^2\right)^2\)
Cho a+b+c=0 CMR : \(\left(a^2+b^2+c^2\right)^2=2\left(a^4+b^4+c^4\right)\)