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1.若x+1/x=3,则x-1/x=2.已知a²+b²+c²=18,ab+bc+ca=13,则(a+b+c)²=以下利用乘法公式计算:5.(a-b+c)·(c+b-a)=6.-3(x+1)·(x-1)+(2x+1)²=7.(3x+2y)*(3x-2y)-(3x-2y)²-(3x+2y)²=8.(2m
题目详情
1.若x+1/x=3,则x-1/x= 2.已知a²+b²+c²=18,ab+bc+ca=13,则(a+b+c)²=
以下利用乘法公式计算:
5.(a-b+c)·(c+b-a)=
6.-3(x+1)·(x-1)+(2x+1)²=
7.(3x+2y)*(3x-2y)-(3x-2y)²-(3x+2y)²=
8.(2m+3)²(2m-3)²
9.(x+y+a-b)*(x-y+a+b)=
以下利用乘法公式计算:
5.(a-b+c)·(c+b-a)=
6.-3(x+1)·(x-1)+(2x+1)²=
7.(3x+2y)*(3x-2y)-(3x-2y)²-(3x+2y)²=
8.(2m+3)²(2m-3)²
9.(x+y+a-b)*(x-y+a+b)=
▼优质解答
答案和解析
1.∵x+1/x=3,
∴(x+1/x)²=9
∴x²+1/x²+2=9
∴x²+1/x²=7
∴(x-1/x)²=x²+1/x²-2=7-2=5
∴x-1/x= ±√5
2
∵a²+b²+c²=18,ab+bc+ca=13,
(a+b+c)²=a²+b²+c²+2(ab+bc+ca)=18+26=44
5.(a-b+c)·(c+b-a)=[c-(b-a)][c+(b-a)]
=c²-(b-a)²=c²-a²-b²+2ab
6.-3(x+1)(x-1)+(2x+1)²
=-3(x²-1)+4x²+4x+1
=x²+4x+4
7.(3x+2y)*(3x-2y)-(3x-2y)²-(3x+2y)²
=9x²-4y²-(9x²-12xy+4y²)-(9x²+12xy+4y²)
=-9x²-12y²
8.(2m+3)²(2m-3)²
=(4m²-9)²
=16m⁴-72m²+81
9.(x+y+a-b)*(x-y+a+b)
=[(x+a)+(y-b)][(x+a)-(y-b)]
=(x+a)²-(y-b)²
=x²+2ax+a²-(y²-2by+b²)
=x²-y²+2ax+2by+a²-b²
∴(x+1/x)²=9
∴x²+1/x²+2=9
∴x²+1/x²=7
∴(x-1/x)²=x²+1/x²-2=7-2=5
∴x-1/x= ±√5
2
∵a²+b²+c²=18,ab+bc+ca=13,
(a+b+c)²=a²+b²+c²+2(ab+bc+ca)=18+26=44
5.(a-b+c)·(c+b-a)=[c-(b-a)][c+(b-a)]
=c²-(b-a)²=c²-a²-b²+2ab
6.-3(x+1)(x-1)+(2x+1)²
=-3(x²-1)+4x²+4x+1
=x²+4x+4
7.(3x+2y)*(3x-2y)-(3x-2y)²-(3x+2y)²
=9x²-4y²-(9x²-12xy+4y²)-(9x²+12xy+4y²)
=-9x²-12y²
8.(2m+3)²(2m-3)²
=(4m²-9)²
=16m⁴-72m²+81
9.(x+y+a-b)*(x-y+a+b)
=[(x+a)+(y-b)][(x+a)-(y-b)]
=(x+a)²-(y-b)²
=x²+2ax+a²-(y²-2by+b²)
=x²-y²+2ax+2by+a²-b²
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