Question

已知a,b,x,y 满足ax + by=3,ay - bx=5,则(a^2 + b^2)(x^2 + y^2)等于___

Answer 1

ax + by=3 (1) ay - bx=5 (2) 显然a,b不同时为0 (1)*a-(2)*b x=(3a-5b)/(a^2+b^2) (1)*b+(2)*a y=(3b+5a)/(a^2+b^2) x^2+y^2=[(3a-5b)/(a^2+b^2)]^2+[(3b+5a)/(a^2+b^2)]^2 =34/(a^2+b^2) (a^2 + b^2)(x^2 + y^2)=(a^2+b^2)*34/(a^2+b^2)=34