Chứng minh rằng

\(\dfrac{a^2}{b}+\dfrac{b^2}{c}+\dfrac{c^2}{a}\ge a+b+c\)

Chứng minh rằng:

\(a^2+b^2+c^2+d^2\ge ab+ac+ad\)

Chứng minh rằng:

a, \(4\left(a^3+b^3\right)\ge\left(a+b\right)^3\) với a> b> 0

b, \(\dfrac{a^2+b^2}{2}\ge\left(\dfrac{a+b}{2}\right)^2\)

c, \(\dfrac{a^2+b^2+c^2}{3}\ge\left(\dfrac{a+b+c}{3}\right)^3\)

Chứng minh rằng :

\(a^2+b^2+c^2+d^2\ge ab+ac+ad\)

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, \(\dfrac{a^2}{b}+\dfrac{b^2}{c}+\dfrac{c^2}{a}\ge a+b+c\)

d, \(a^2+b^2+c^2+d^2\ge ab+ac+ad\)