Question

已知a-b=5,b-c=3,求a平方+b平方+c平方=ab-ac-bc

Answer 1

解：
a-b=5,b-c=3
两式相加
a-c=8
∴a²+b²+c²-ab-ac-bc吧
=a(a-b)+b(b-c)+c(c-a)
=a*5+b*3+c*(-8)
=5(a-c)+3(b-c)
=5*8+3*3
=40+9
=49

Answer 2

解：由已知两式相加得a-c=8
a²+b²+c²-ab-bc-ac
=1/2(2a²+2b²+2c²-2ab-2bc-2ac)
=1/2［(a-b)²+(b-c)²+(a-c)²］
=1/2(5²+3²+8²）
=1/2×100
=50