Question

已知a减b等于根号3加根号2，b减c等于根号3减根号2，求a平方加b平方加c平方减ab减ac减bc

Answer 1

因为a-b=√3+√2，b-c==√3-√2，两式相加得到a-c=2√3

（a-b）^2=5+2√6
（b-c）^2=5-2√6
（a-c）^2=12
原式=1/2(a^2+b^2-2ab+a^2+c^2-2ac+b^2+c^2-2bc )
=1/2[（a-b）^2+（b-c）^2+（a-c）^2]
=1/2 (5+2√6+5-2√6+12)
=1/2 x 22
=11

Answer 2

解：因为a-b=√3+√2，b-c==√3-√2，两式相加得到a-c=2√3，而a²+b²+c²-ab-ac-bc=
1/2[(a-b)²+(b-c)²+(a-c)²]=1/2(3+2+2√6+3+2-2√6+12)=1/2×22=11

Answer 3

a平方加b平方加c平方减ab减ac减bc=1/2(a-b)^2+1/2(a-c)^2+1/2(a-c)^2=1/2(根号3加根号2)+1/2(根号3减根号2)+1/2(2根号2)=9