## a*b*c*d*e = 1 & a^4 + b^4 + c^4 + d^4 + e^4 ≥ a + b + c + d + e

Given   $a, b, c, d, e > 0$,           $a\cdot b \cdot c\cdot d \cdot e = 1$,

show that

$a^4 + b^4 + c^4 + d^4 + e^4 \; \geq \; a + b + c + d + e$

Find as many diferent solutions as you can.