Các câu hỏi tương tự
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 bất đẳng thức
a)\(8\left(a^4+b^4\right)\ge\left(a+b\right)^4\)
b)\(\left(a^2+b^2\right)^2\ge ab\left(a+b\right)^2\)
1. CM: \(3\left(a^2+b^2\right)-ab+4\ge2\left(a\sqrt{b^2+1}+b\sqrt{a^2+1}\right)\)
2. CMR: \(a^4+b^4+c^4+1\ge2a\left(ab^2-a+c+1\right)\)
3. Cm: \(\left(a^5+b^5\right)\left(a+b\right)\ge\left(a^4+b^4\right)\left(a+b\right)\)
cm
\(a^4+b^4\ge\frac{\left(a+b\right)^4}{8}\)
CMR: \(8\left(a^4+b^4\right)\ge\left(a+b\right)^4\)
a, b, c \(\ge\)0. CM: \(\frac{a^3+b^2+c}{3}\ge abc+\frac{3I\left(a-b\right)\left(b-c\right)\left(c-a\right)I}{4}\)
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 \(a,b,c>0.\)\(Cmr:\frac{a^4}{\left(a+b\right)\left(a^2+b^2\right)}+\frac{b^4}{\left(b+c\right)\left(b^2+c^2\right)}+\frac{c^4}{\left(c+a\right)\left(c^2+a^2\right)}\ge\frac{a+b+c}{4}\)
CM B=3A với:
\(B=4^{32}+1\)
\(A=\left(4+1\right)\left(4^2+1\right)\left(4^4+1\right)\left(4^8+1\right)\left(4^{16}+1\right)\)