由算術-調和平均不等式。
5/(x+y+1) = 5[1/(x+y+(1/3)+(1/3)+(1/3)] <= (5/25)[1/x + 1/y + 3 + 3 + 3]
=(1/5)(1/x + 1/y) + 9/5
代入右邊，移項化簡。不等式的證明歸結於證明
1/x + 1/y + 1/z >= 9.
LHS >= 3/cuberoot(xyz) >= 3/((x+y+z)/3) = 9.
5/(x+y+1) = 5[1/(x+y+(1/3)+(1/3)+(1/3)] <= (5/25)[1/x + 1/y + 3 + 3 + 3]
=(1/5)(1/x + 1/y) + 9/5
代入右邊，移項化簡。不等式的證明歸結於證明
1/x + 1/y + 1/z >= 9.
LHS >= 3/cuberoot(xyz) >= 3/((x+y+z)/3) = 9.
選擇“Disable on www.wenxuecity.com”
選擇“don't run on pages on this domain”
