悬赏!几道八年级因式分解的数学题1.因式分解:2a(x²+1)²-2ax²2.83²-83×34+17²=3.已知x²-y²=12,x-y=2,则x/y=4.已知x+1/x=3,那么x的四次方加X的四次方分之一=5.已知a²+b²+2a-4b+5=0,求的2a²+4b-3值6.已知x+y=1,则1/2 x² +xy+1/2 y²=

问题描述:

悬赏!几道八年级因式分解的数学题
1.因式分解:2a(x²+1)²-2ax²
2.83²-83×34+17²=
3.已知x²-y²=12,x-y=2,则x/y=
4.已知x+1/x=3,那么x的四次方加X的四次方分之一=
5.已知a²+b²+2a-4b+5=0,求的2a²+4b-3值
6.已知x+y=1,则1/2 x² +xy+1/2 y²=

1.2a(X²+1+X)(X²+1-X)
2.83²-83×17-83×17+17²=83(83-17)+17(17-83)=83(83-17)-17(83-17)=(83-17)²
3.X²-Y²=(X+Y)(X-Y)=12 ∵X-Y=2∴ X+Y=6 ,解二元一次方程得X=4,Y=2,∴X/Y=2
4.∵x+1/x=3,∴(x+1/x)²=9,x²+1/x²=9-2,∵(x²+1/x²)²=49,x四次方+1/x四次方=49-2=47
5.=(a²+2a+1)+(b²-4b+4)=(a+1)²+(b-2)²=0。∵完全平方数一定>0且(a+1)²+(b-2)²=0,∴a=-1,b=2,∴2a²+4b-3=2+8-3=7
6.1/2 x² +xy+1/2 y²=1/2(x²+y²+2xy)=1/2(X+Y)²,又∵x+y=1,∴1/2 x² +xy+1/2 y²=1/2

1)
2a(x²+1)²-2ax²=2a((x²+1)²-x²)=2a(x²+x+1)(x²-x+1)
2)
83²-83×34+17²=(83-17)²=66²=4356=2²3²11²
3)
x²-y²=(x+y)(x-y)=2(x+y)=12
x-y=2
x+y=6
x=4,y=2
x/y=2
3)
x+1/x=3
两边平方
x²+1/x²=7
两边平方
x的四次方加X的四次方分之一=47
4)
a²+b²+2a-4b+5=(a+1)²+(b-2)²=0
a=-1
b=2
2a²+4b-3=2*(-1)²+4*2-3=7
5)
1/2 x² +xy+1/2 y²==1/2(x+y)²=1/2

答案如下:
1.2a(x²+1)²-2ax² = 2a[(x²+1)² - x²] = 2a[(x²)² + 2 x² + 1 - x²] = 2a[(x²)² + x² + 1 ]
2.83²-83×34+17² = 83²- 2 x 83×17+17² = (83 - 17)² = 66²
3.x²-y²=(x-y)*(x + y)= 12
x-y=2 所以 x+ y = 6 解方程得 x = 4, y = 2; 则x/y= 2
4.x+1/x=3,则[x+1/x]² = x² + 2(x * 1/x) + (1/x)² = x² + 2+ (1/x)² = 9,推出x² +(1/x)² = 7
【x² +(1/x)²】² = (x²)² + 2 + [(1/x)²]² = 49,则(x²)² + [(1/x)²]² = 47
5.a²+b²+2a-4b+5=a²+2a+1 + b²-4b+4= (a + 1)² + (b - 2)² = 0 平方不能小于0,所以(a + 1)² =0,(b - 2)² = 0,推出 a= -1, b = 2;则2a²+4b-3 = 2 + 4 - 3 = 3
6.已知x+y=1,则1/2 x² +xy+1/2 y²=1/2 [x² +2xy+y²] = 1/2 (x + y)² = 1/2

1. 2a(x²+1+x)(x²-x+1)
2. 83²-83×34+17²=83²-2×83×17+17²=(83-17)²=4356
3 (x+y)(x-y)=12 x-y=2 x+y=6 x=4 y=2 x/y=2
4. x^4+1/x^4=x^4+1/x^4+2-2=(x²+1/x²)²-2=[(x+1/x)²-2]²-2=47
5.(a+1)²+(b-2)²=0 a=-1 b=2 2a²+4b+3=13
6. 1/2(x²+2xy+y²)=1/2(x+y)²=1/2

1.=2a((x²+1)²-x²)= 2a(x²+x+1)(x²-x+1)2.原式=83²-2*83*17+17²=(83-17)²=66²3.(x-y)(x+y)=x²-y²=12 ∵(x-y)=2 ∴x+y=6 ∴x=4 y=2 ∴x/y=24.∵x+1/x=3 ∴(x...

1 2a(x2+1+x)(x2+1-x)

1. =2a(x4+x2+1)
2. =(83-17)2
3. 2
4. 16+1/16
5. (a+1)2+(b-2)2=0,故a=-1,b=2,故值为7
6. =1/2(x+y)2=1/2