Question

Fie a,b,c,d,x,y numere naturale nenule astfel incat a supra b = c supra d si a * y = b * x. Aratati ca a supra c + x = b supra d + y.

Answer 1

Răspuns:

a/b=c/d

a×y=b×x =>a/b=x/y=c/d

(a+x+c)/(b+y+d)=a(d+y)+ab+

x(b+y+d)+c(d+y)+cd=

(d+y)(a+c)+ab+cd+xb+xy+xd=

(d+y)(a+c)+ab+cd+ay+xy+xd=

(d+y)(a+c)+ab+cd+ay+x(y+d)=

=>a/(c+x)=b/(d+y)