Question

化简求值：已知x²-2x=2,求代数式（x-1)²+(x+3)(x-3)+(x-3)(x-1)的值

Answer 1

（x-1)²+(x+3)(x-3)+(x-3)(x-1)
=x²-2x+1+x²-9+x²-4x+3
=3x²-6x+13
=3(x²-2x)+13 [x²-2x=2代入式子]
=3*2+13
=19

Answer 2

∵x²-2x=2
∴x²-2x+1=3即（x-1）²=3
原式=（x-1)²+(x+3)(x-3)+(x-3)(x-1)
=（x-1）²+(x-3)(x+3+x-1)
=(x-1)²+2(x-3)(x+1)
=(x-1)²+2(x²-2x-3)
=3+2×（-1）
=1