Question

先化简，后求值。已知x的2次方-2x=3,求代数式(x-1)的2次方+(x+2)(x-2)+(x-3)(x-1)的值

Answer 1

x²-2x=3
x²-2x-3=0
(x-3)(x+1)=0
x=-1或x=3
(x-1)²+(x+2)(x-2)+(x-3)(x-1)
=(x-1)(x-1+x-3)+(x+2)(x-2)
=2(x-1)(x-2)+(x+2)(x-2)
=(x-2)(2x-2+x+2)
=3x(x-2)
当x=-1时，上式=9
当x=3时，上式=9
综上所述：代数式=9
希望帮助到你，望采纳，谢谢~

Answer 2

(x-1)的2次方+(x+2)(x-2)+(x-3)(x-1)
=(x-1)²+(x-3)(x-1)+(x+2)(x-2)
=(x-1)(x-1+x-3)+(x+2)(x-2)
=(x-1)(2x-4)+(x+2)(x-2)
=(2x-2)(x-2)+(x+2)(x-2)
=(x-2)(2x-2+x+2)
=3x(x-2)
=3(x²-2x)
=3×3
=9

Answer 3

代数式提取公因式（x-1）原式变成(x-1)(x-1+x-3)+(x+2)(x-2)=2(x-1)(x-2)+(x+2)(x-2)=(x-2)(2x-2+x+2)=3x(x-2) 由已知式x(x-2)=3 则原式=9