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x^a + x^d>= x^b + x^c , for x>0 if a>b>c>d >= q 0 and a + d = b + c

Source: 1978 Swedish Mathematical Competition p1

March 26, 2021

inequalitiesalgebra

Problem Statement

Let

a,b,c,d

be real numbers such that

a>b>c>d\geq 0

and

a + d = b + c

. Show that

x^a + x^d \geq x^b + x^c

for

x>0