一个数学题目，求高手解答，，，比较(x-3)²与(x-2)(x-4)两个代数式的大小，并证明结论.

Question

如题所述

Answer 1

因为(x-3)²-(x-2)(x-4)=x²-6x+9-(x²-6x+8)=9-8=1>0
所以(x-3)²>(x-2)(x-4)

Answer 2

(x-3)²-(x-2)(x-4)

=x^2-6x+9-(x^2-6x+8)
=x^2-6x+9-x^2+6x-8
=1>0
∴(x-3)²>(x-2)(x-4)

Answer 3

(x-2)(x-4)
=[(x-3)+1][(x-3)-1]
=(x-3)^2-1

(x-3)²-(x-2)(x-4)

=(x-3)²-[(x-3)^2-1]
=1

所以(x-3)²>(x-2)(x-4)

Answer 4

(x - 3)^2 - (x - 2) * (x - 4)
= x^2 - 6 * x + 9 - x^2 + 6 * x -8
= 1 > 0
所以(x - 3)^2 > (x - 2) * (x - 4)

Answer 5

两个代数式相减，你试试能不能解