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Cho \(a,b,c>0.\)\(Cmr:\frac{a^4}{\left(a+b\right)\left(a^2+b^2\right)}+\frac{b^4}{\left(b+c\right)\left(b^2+c^2\right)}+\frac{c^4}{\left(c+a\right)\left(c^2+a^2\right)}\ge\frac{a+b+c}{4}\)
Cho a+b+c=0 CMR
\(a^5.\left(b^2+c^2\right)+b^5.\left(c^2+a^2\right)+c^5.\left(a^2+b^2\right)=\frac{1}{2}.\left(a^3+b^3+c^3\right).\left(a^4+b^4+c^4\right)\)
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 : \(\left(a^2+b^2+c^2\right)^2=2\left(a^4+b^4+c^4\right)\)
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
\(\left(a^2+b^2+c^2\right)=2\left(a^4+b^4+c^4\right)\)
Giải hộ t bài này (đáng tiếc thầy giáo k cho dùng cauchy ức chế vãi linh hồn, đừng ai dùng cauchy nhé)
Cho a,b,c > 0. CMR
\(\frac{a^4}{\left(a+b\right)\left(a^2+b^2\right)}+\frac{b^4}{\left(b+c\right)\left(b^2+c^2\right)}+\frac{c^4}{\left(c+a\right)\left(c^2+a^2\right)}\ge\frac{a+b+c}{4}\)
1)cho a + b + c = 0 CMR
\(\left(a^2+b^2+c^2\right)^2=2\left(a^4+b^4+c^4\right)\)
a) Cho \(x^2+y^2+z^2=xy+yz+zx\). CMR : x=y=z
b) cho \(\left(a-b\right)^2+\left(b-c\right)^2+\left(c-a\right)^2+4\left(ab+ac+bc\right)=4\left(a^2+b^2+c^2\right)\). CMR : a=b=c