1 1025^2-1023*1027=?求简便方法,
1个回答

① 1025²-1203×1207

=1025²-(1205-2)×(1205+2)

=1025²-(1025²-4)

=1025²-1025²+4

=4

② 设 a²+b²+c²-ab-bc-ac= y

两边同×2,得

2a²+2b²+2c²-2ab-2bc-2ac = 2y

(a²-2ab+b²)+(b²-2bc+c²)+(a²-2ac+c²) = 2y

(a-b)²+(b-c)²+(a-c)² = 2y

∵a-b=-1, b-c=-1, c-a=2

∴原式 1+1+4=2y

6=2y

y=3

答:结果是3.

③ x+1 x+1 2x-3

3 × 5 = 15

x+1 2x-3

15 =15

∴ x+1 = 2x-3

4 = x

x = 4

答:x的值为4.