Các câu hỏi tương tự
Cm \(8\left(a^4+b^4\right)\ge\left(a+b\right)^4\)
a, b, c \(\ge\)0. CM: \(\frac{a^3+b^2+c}{3}\ge abc+\frac{3I\left(a-b\right)\left(b-c\right)\left(c-a\right)I}{4}\)
cm:\(\left(a^{10}+b^{10}\right)\left(a^2+b^2\right)\ge\left(a^8+b^8\right)\left(a^4+b^4\right)\)
ai giải giúp bài này với!
Chứng minh rằng
a, \(2\left(a^4+b^4\right)\ge\left(a+b\right)\left(a^3+b^3\right)\))
b, \(3\left(a^4+b^4+c^4\right)\ge\left(a+b+c\right)\left(a^3+b^3+c^3\right)\)
c, \(\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a}\ge a+b+c\)
Cho a,b,c>0. CM: \(\frac{a^4+b^4+c^4}{ab+bc+ca}+\frac{3abc}{a+b+c}\ge\frac{2}{3}.\left(a^2+b^2+c^2\right)\)
1. Chứng minh răng \(\left(\frac{a}{a+b}\right)^4+\left(\frac{b}{b+c}\right)^4+\left(\frac{c}{c+d}\right)^4+\left(\frac{d}{d+a}\right)^4\)\(\ge\frac{1}{4}\)
CM: c(a+b) \(\ge\frac{\left(a+b+c\right)^2}{4}\)
Cho \(a,b,c>0.\)\(Cmr:\frac{a^4}{\left(a+b\right)\left(a^2+b^2\right)}+\frac{b^4}{\left(b+c\right)\left(b^2+c^2\right)}+\frac{c^4}{\left(c+a\right)\left(c^2+a^2\right)}\ge\frac{a+b+c}{4}\)
Cm:
\(\frac{1}{a}+\frac{1}{b}\ge\frac{4}{a+b}\left(a,b\ne0\right)\)
Không dùng S.vac