Question

chứng minh các bất đẳng thức sau:

a) \(\frac{a^4}{b}+\frac{b^4}{c}+\frac{c^4}{a}\ge3abc,\left(\forall a,b,c>0\right)\)

b) \(\left(\frac{a+b+c+d}{4}\right)^4\ge abcd,\left(\forall a,b,c,d\ge0\right)\)

c) \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ge\frac{9}{a+b+c},\left(\forall a,b,c>0\right)\)

d) \(\frac{a+b}{c}+\frac{b+c}{a}+\frac{c+a}{b}\ge6,\left(\forall a,b,c>0\right)\)

Answer 1

https://i.imgur.com/bx8s8Hy.jpg

Answer 2

https://i.imgur.com/AISWXxC.jpg