Let
f(a,b,c,d)=(a²+1)(b²+1)(c²+1)(d²+1)/abcd
=(a²+1)/a * (b²+1)/b *(c²+1)/c * (d²+1)/d
What is a positive integer?
It is a member of the set {1,2,3,4.....}
So the smallest positive integer is 1.
Consider the factor
(a²+1)/a
=a+1/a
≥2 when a≥1
therefore
f(a,b,c,d)≥16 when a,b,c,d ∈Z+
Show that a,b,c, and d are positive integers when,
((a^2+1)(b^2+1)(c^2+1)(d^2+1))/abcd≥16
1 answer
1 answer