问题
解答题
比较大小有求差、求比等方法,但灵活应用已知巧妙变形也会起到简化计算的效果.已知a、b为实数,且ab=1,设P=
|
答案
P=
+a a+1 b b+1
=a(b+1)+b(a+1) (a+1)(b+1)
=2ab+a+b (a+1)(b+1)
=
,a+b+2 (a+1)(b+1)
Q=
+1 a+1 1 b+1
=
,a+b+2 (a+1)(b+1)
则P=Q.
比较大小有求差、求比等方法,但灵活应用已知巧妙变形也会起到简化计算的效果.已知a、b为实数,且ab=1,设P=
|
P=
+a a+1 b b+1
=a(b+1)+b(a+1) (a+1)(b+1)
=2ab+a+b (a+1)(b+1)
=
,a+b+2 (a+1)(b+1)
Q=
+1 a+1 1 b+1
=
,a+b+2 (a+1)(b+1)
则P=Q.