Question

①当y=3x-2时，则代数式3x²-2xy+1/3y²-1的值为多少？②若3的m次方=2，9的n次方=5，

则3的2m-4n+1等于多少？

Answer 1

1. ∵y=3x-2 ∴3x-y=2
3x²-2xy+1/3y²-1
=1/3(9x²-6xy+y²)-1
=1/3(3x-y)²-1
=1/3
2. ∵9的次方=5 ∴3的2n次方=5
3的2m-4n+1次方
=3的2m次方*3的-4n次方*3
=3的m次方的平方*3的2n的-2 次方*3
=4*1/25*3
=12/25

Answer 2

①3x²-2xy+1/3y²-1
=3x²-2x(3x-2)+1/3 (3x-2)²-1
=3x²-6x²+4x+3x²-4x-4/3-1
=-7/3
②3^m=2 9^n=5→3^(2n)=5
3^(2m-4n+1)=3^(2m)÷3^(4n)×3=(3^m)²÷(3^2n)²×3=2²÷5²×3=12/25

追问

你算错啦~应该是
3x²-6x²+4x+3x²-4x+4/3-1
=1/3

追答

①3x²-2xy+1/3y²-1
=3x²-2x(3x-2)+1/3 (3x-2)²-1
=3x²-6x²+4x+3x²-4x+4/3-1
=1/3
是的，谢谢提醒