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> 已知a-b=3+2,b-c=3-2,求a2+b2+c2-ab-bc-ca的值.-数学
已知a-b=3+2,b-c=3-2,求a2+b2+c2-ab-bc-ca的值.-数学
题目简介
已知a-b=3+2,b-c=3-2,求a2+b2+c2-ab-bc-ca的值.-数学
题目详情
已知a-b=
3
+
2
,b-c=
3
-
2
,求a
2
+b
2
+c
2
-ab-bc-ca的值.
题型:解答题
难度:中档
来源:不详
答案
∵a-b=
3
+
2
①,b-c=
3
-
2
②,
∴①+②得:a-c=2
3
,
∴a2+b2+c2-ab-bc-ca=
class="stub"1
2
(2a2+2b2+2c2-2ab-2bc-2ca)
=
class="stub"1
2
[(a2-2ab+b2)+(a2-2ac+c2)+(b2-2bc+c2)]
=
class="stub"1
2
[(a-b)2+(a-c)2+(b-c)2]
=
class="stub"1
2
×[(
3
+
2
)2+(2
3
)2+(
3
-
2
)2]
=
class="stub"1
2
×[5+2
6
+12+5-2
6
]
=11.
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题目简介
已知a-b=3+2,b-c=3-2,求a2+b2+c2-ab-bc-ca的值.-数学
题目详情
答案
∴①+②得:a-c=2
∴a2+b2+c2-ab-bc-ca=
=
=
=
=
=11.