Question

a—b=2,a—c=1,求(2a—b—c)的平方加上(c—a)的平方,值为多少?

Answer 1

原式=4a2-4a(b+c)+(b+c)2+(c-b)2

=4a2-4ab-4ac+2b2+2c2

∵ a-b=2,a-c=1

∴b=a-2 c=a-1

原式=4a2-4a(a-2)-4a(a-1)+2(a-2)2+2(a-1)2

=8a-4a2+4a+2a2-8a+8+2a2-4a+2

=10

(字母后面的2为平方)