Question

[Mạc Thiên Tử]

chứng minh rằng :

a, x+2y+\(\dfrac{25}{x}\)+\(\dfrac{27}{y^2}\)\(\ge\) 19 ( \(\forall\)x,y \(\)> 0 )

b, \(x+\dfrac{1}{\left(x-y\right)y}\ge3\) ( \(\forall\)x>y>0 )

c,\(\dfrac{x}{2}+\dfrac{16}{x-2}\ge13\left(\forall x>2\right)\)

d, \(a+\dfrac{1}{a^2}\ge\dfrac{9}{4}\left(\forall x\ge2\right)\)

e, a+\(\dfrac{1}{a\left(a-b\right)^2}\ge2\sqrt{2}\) ( \(\forall x>y\ge0\))

f, \(\dfrac{2a^3+1}{4b\left(a-b\right)}\ge3[\forall a\ge\dfrac{1}{2};\dfrac{a}{b}>1]\)

g, x+\(\dfrac{4}{\left(x-y\right)\left(y+1\right)^2}\ge3\left(\forall x>y\ge0\right)\)

h, \(2a^4+\dfrac{1}{1+a^2}\ge3a^2-1\)