Question

已知a-b=√3+√2,b-c=√3-√2,求a的平方+b的平方+c的平方-ab-ac-bc的值.

Answer 1

a-b=√3+√2,b-c=√3-√2

相加

a-c=2√3

a²+b²+c²-ab-bc-ac

=(2a²+2b²+2c²-2ab-2bc-2ac)/2

=[(a²-2ab+b²)+(b²-2bc+c²)+(c²-2ac+a²)]/2

=[(a-b)²+(b-c)²+(c-a)²]/2

=(3+2√6+2+3-2√6+2+12)/2

=11