1、(xy)²-3xy-10
=(xy-5)(xy+2)
2. x²-y²+y-¼
=x²-(y²-y+1/4)
=x²-(y-1/2)²
=(x+y-1/2)(x-y+1/2)
3. 已知x²-5x-1=0,求x-(x分之一),x²+(x²分之一)的值
x²-5x-1=0,得x²-1=5x
同除x得:x-1/x=5
(x-1/x)²=25
得x²+1/x²=23
4. 填空:1x2x3x4+1=(5 )²;
2x3x4x5+1=( 11 )²
11x12x13x14+1=(155 )²
36x37x38x39+1=( 1405 )²
用你学过的文字语言概括以上算式的规律(四个连续自然数的乘积加1等于中间二数乘积减1的平方 )
并用学过的因式分解的知识来说明这个规律。
x(x+1)(x+2)(x+3)+1
=x(x+3)(x+1)(x+2)+1
=(x²+3x+2-2)(x²+3x+2)+1
=(x²+3x+2)²-2(x²+3x+2)+1
=(x²+3x+2)²
=((x+1)(x+2))²