Question

若a减b等于2加根号3,b减c等于2减根号3试求a平方加b平方加c平方减ab减bc减ca的值

Answer 1

a-b=2+√3
b-c=2-√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