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> 已知a2+2a=8,则1a+1-1a2-1÷a+1a2-2a+1的值为______.-数学
已知a2+2a=8,则1a+1-1a2-1÷a+1a2-2a+1的值为______.-数学
题目简介
已知a2+2a=8,则1a+1-1a2-1÷a+1a2-2a+1的值为______.-数学
题目详情
已知a
2
+2a=8,则
1
a+1
-
1
a
2
-1
÷
a+1
a
2
-2a+1
的值为______.
题型:填空题
难度:偏易
来源:不详
答案
原式=
class="stub"1
a+1
-
class="stub"1
(a+1)(a-1)
×
(a-1
)
2
a+1
=
class="stub"1
a+1
-
class="stub"a-1
(a+1
)
2
=
class="stub"2
(a+1)
2
,
∵a2+2a=8,
∴(a-2)(a+4)=0,解得a1=2,a2=-4,
当a=2时,原式=
class="stub"2
(2+1)
2
=
class="stub"2
9
;
当a=-4时,原式=
class="stub"2
(-4+1)
2
=
class="stub"2
9
.
故答案为:
class="stub"2
9
.
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题目简介
已知a2+2a=8,则1a+1-1a2-1÷a+1a2-2a+1的值为______.-数学
题目详情
答案
=
=
∵a2+2a=8,
∴(a-2)(a+4)=0,解得a1=2,a2=-4,
当a=2时,原式=
当a=-4时,原式=
故答案为: