Question

已知a-b=3,b-c=4,求a的平方+b的平方+c的平方-ab-bc-ac的值

Answer 1

a-b=3

b-c=4

以上两式相加：a-c=7

a^2+b^2+c^2-ab-bc-ac

= 1/2 {2a^2+2b^2+2c^2-2ab-2bc-2ac}

= 1/2 {(a-b)^2+(b-c)^2+(a-c)^2}

= 1/2 {3^2+4^2+7^2}

= 1/2 * 74

= 37