MHB Can the Inequality $x,y,z>1$ be Proven with a Hint of 48?

[Albert1]

$x,y,z>1$

please prove :

$\dfrac{x^4}{(y-1)^2}+\dfrac{y^4}{(z-1)^2}+\dfrac{z^4}{(x-1)^2}\geq 48$

 

[Albert1]

$x,y,z>1$

please prove :

$\dfrac{x^4}{(y-1)^2}+\dfrac{y^4}{(z-1)^2}+\dfrac{z^4}{(x-1)^2}\geq 48$

hint:

Spoiler

prove :$\dfrac{x^4}{(y-1)^2}\geq 32(x-y)+16$

 

[Albert1]

hint:

Spoiler

prove :$\dfrac{x^4}{(y-1)^2}\geq 32(x-y)+16$

Spoiler

$\dfrac{x^4}{(y-1)^2}+16(y-1)+16(y-1)+16\geq 4\sqrt[4]{16^3x^4}= 32x$
or :$\dfrac{x^4}{(y-1)^2}\geq 32(x-y)+16$
please complete the rest