化简,求值.(1)先化简,再求值:(x+3)(x-3)-x(x-2),其中x=4;(2)先化简,再求值:(2a-b)2-b2,其中a=2,b=3;(3)已知210=a2=4b,化简(14a+15b)•

题目简介

化简,求值.(1)先化简,再求值:(x+3)(x-3)-x(x-2),其中x=4;(2)先化简,再求值:(2a-b)2-b2,其中a=2,b=3;(3)已知210=a2=4b,化简(14a+15b)•

题目详情

化简,求值.
(1)先化简,再求值:(x+3)(x-3)-x(x-2),其中x=4;
(2)先化简,再求值:(2a-b)2-b2,其中a=2,b=3;
(3)已知210=a2=4b,化简(
1
4
a+
1
5
b)•(
1
4
a-
1
5
b)-(
1
4
a+
1
5
b)2
,并求值.
题型:解答题难度:中档来源:不详

答案

(1)(x+3)(x-3)-x(x-2)
=x2-9-x2+2x
=2x-9,
把x=4代入原式得:原式=2×4-9=-1;

(2)(2a-b)2-b2
=4a2-4ab+b2-b2
=4a2-4ab,
把a=2,b=3代入原式得:原式=4×22-4×2×3=4×4-24=-8;

(3)∵210=a2,
∴(25)2=a2,
∴a=±32,
∵210=4b,
∴(25)2=45=4b,
∴b=5,
(class="stub"1
4
a+class="stub"1
5
b)•(class="stub"1
4
a-class="stub"1
5
b)-(class="stub"1
4
a+class="stub"1
5
b)2

=(class="stub"1
4
a)2-(class="stub"1
5
b)2-(class="stub"1
4
a)2-(class="stub"1
5
b)2-2×class="stub"1
4
class="stub"1
5
b
=-class="stub"1
10
ab-class="stub"2
25
b2,
∴原式=-class="stub"1
10
ab-class="stub"2
25
b2=-class="stub"1
10
×32×5-class="stub"2
25
×52=-18或=-class="stub"1
10
×(-32)×5-class="stub"2
25
×52=14.

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