a√a -a√b +b√a √ab-b
1个回答

是不是

(a√a -a√b +b√a)/(a√a+b√b )+[√(ab)-b)]/(a-b)

设x=√a ,y=√b

(a√a -a√b +b√a)/(a√a+b√b )+[√(ab)-b)]/(a-b)

=(x^3-x^2*y+x*y^2)/(x^3+y^3)+(xy-y^2)/(x^2-y^2)

=x*(x^2-xy+y^2)/[(x+y)*(x^2-xy+y^2)]+y*(x-y)/[(x+y)*(x-y)]

=x/(x+y)+y/(x+y)

=(x+y)/(x+y)

=1