(1)计算:(-2a)2-(a-2)(a-6)(2)[(x-2y)2-(x-2y)(x+2y)]÷4y(3)已知ABC的三边分别是a=m2-n2,b=2mn,c=m2+n2.试判断ABC是否是直角三角

题目简介

(1)计算:(-2a)2-(a-2)(a-6)(2)[(x-2y)2-(x-2y)(x+2y)]÷4y(3)已知ABC的三边分别是a=m2-n2,b=2mn,c=m2+n2.试判断ABC是否是直角三角

题目详情

(1)计算:(-2a)2-(a-2)(a-6)
(2)[(x-2y)2-(x-2y)(x+2y)]÷4y
(3)已知ABC的三边分别是a=m2-n2,b=2mn,c=m2+n2.试判断ABC是否是直角三角形.
题型:解答题难度:中档来源:不详

答案

(1)(-2a)2-(a-2)(a-6)
=4a2-(a2-6a-2a+12)
=4a2-a2+6a+2a-12
=3a2+8a-12;

(2)[(x-2y)2-(x-2y)(x+2y)]÷4y
=[(x2-4xy+4y2)-(x2-4y2)]÷4y
=[x2-4xy+4y2-x2+4y2]÷4y
=[8y2-4xy]÷4y
=2y-x;

(3)∵(m2-n2)2+(2mn)2
=m4+n4-2m2n2+4m2n2
=m4+n4+2m2n2
=(m2+n2)2,
∴a2+b2=c2,
∴三角形ABC是直角三角形.

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