Question

已知a-b=2+根号3，b-c=2-根号3，求a方+b方+c方-ab-bc-ac的值

Answer 1

解：由a-b=2+根号3，① b-c=2+根号3，②
①+②，得，a-c=4 ③
a²+b²+c²-ab-bc-ac
=(1/2a²-ab+1/2b²)+(1/2b²-bc+1/2c²)+(1/2a²-ac+1/2c²)
=1/2(a-b)²+1/2(b-c)²+1/2(a-c)²
=1/2[(a-b)²+(b-c)²+(a-c)²]
将①，②，③代入上式，得
.a²+b²+c²-ab-bc-ac
=1/2[(a-b)²+(b-c)²+(a-c)²]
=1/2[(2+根号3)²+（2-根号3)²+4²]
=(1/2)×30=15

Answer 2

不会吗？
解：由a-b=2+根号3，① b-c=2+根号3，②
①+②，得，a-c=4 ③
a²+b²+c²-ab-bc-ac
=(1/2a²-ab+1/2b²)+(1/2b²-bc+1/2c²)+(1/2a²-ac+1/2c²)
=1/2(a-b)²+1/2(b-c)²+1/2(a-c)²
=1/2[(a-b)²+(b-c)²+(a-c)²]
将①，②，③代入上式，得
.a²+b²+c²-ab-bc-ac
=1/2[(a-b)²+(b-c)²+(a-c)²]
=1/2[(2+根号3)²+（2-根号3)²+4²]
=(1/2)×30=15