已知ax＋ x/(x-1)>b,a,b为正实数,x>1证明√a ＋1>√b

题目

已知ax＋ x/(x-1)>b,a,b为正实数,x>1证明√a ＋1>√b

答案

ax+1/(x-1)>b-1
a(x-1)+1/(x-1)>b-a-1
a(x-1)+1/(x-1)>=2√a>b-a-1
b