已知A-B=2,A-C=1,求(2A-B-C)方+(C-A)方

问题描述:

已知A-B=2,A-C=1,求(2A-B-C)方+(C-A)方

(2A-B-C)^2+(C-A)^2=((A-B)+(A-C))^2+(A-C)^2=(2+1)^2+1=10

(2A-B-C)²+(C-A)²
=(A-B+A-C)²+(A-C)²
=(A-B)²+2(A-B)(A-C)+(A-C)²+(A-C)²
=2²+2*2*1+1²+1²
=4+4+1+1
=10

(2A-B-C)方+(C-A)方
=((A-B)+(A-C))方+(-(A-C))方
=(2+1)方+(-1)方
=9+1
=10

(2A-B-C)^2+(C-A)^2
=[ (A-B)+(A-C) ]^2+(A-C)^2
=(2+1)^2+1^2
=3^2+1
=9+1
=10