已知a-b=2+根号3,b-c=2-根号3,则a平方+b平方+c平方-ab-ac-bc的值为多少

2024-12-20 19:03:13
推荐回答(3个)
回答1:

a-b=2+根号3,b-c=2-根号3

相加
a-c=4

原式= (2a²+2b²+2c²-2ab-2bc-2ac)/2
=[(a²-2ab+b²)+(b²-2bc+c²)+(c²-2ac+a²)]/2
=[(a-b)²+(b-c)²+(a-c)²]/2
=(7+4√3+7-4√3+16)/2
=15

回答2:

a-b=2+根号3,b-c=2-根号3

a-c=4
a平方+b平方+c平方-ab-ac-bc

=1/2[(a-b)^2+(b-c)^2+(a-c)^2]
=1/2(7+4√3+7-4√3+16)
=15

回答3:

15