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.