3.閱讀材料,解答問(wèn)題:
已知實(shí)數(shù)m,n滿足m
2-m-1=0,n
2-n-1=0,且m≠n,則m,n是方程x
2-x-1=0的兩個(gè)不相等的實(shí)數(shù)根,由韋達(dá)定理可知m+n=1,mn=-1.
根據(jù)上述材料,解決以下問(wèn)題:
(1)直接應(yīng)用:已知實(shí)數(shù)a,b滿足:a
2-7a+1=0,b
2-7b+1=0且a≠b,則a+b=
,ab=
;
(2)間接應(yīng)用:在(1)條件下,求
+
的值;
(3)拓展應(yīng)用:已知實(shí)數(shù)m,n滿足:
+
=7,n
2-n=7且mn+1≠0,則
-n=
.