Question

Dacă 5/x=8/y , calculează: a) x+y/y-x ; b) x la puterea a doua + y la puterea a doua / x×y​

Answer 1

Răspuns:

a) 13/3; b) 89/40.

Explicație pas cu pas:

5/x=8/y => 8x=5y adica x=5y/8

a)

calculam numaratorul: x+y=5y/8+y=13y/8

calculam numitorul: y-x=y-5y/8=3y/8

(x+y)/(y-x)=(13y/8):(3y/8)=13y/8*8/3y=13/3

b) calculam numaratorul:  (^2 inseamna ridicat la puterea a2-a

iar * =inmultire)

x^2+y^2=(5y/8)^2+y^2=25y^2/64+y^2=89y^2/64

calculam numitorul: x*y=5y/8*y=5y^2/8

(x^2+y^2)/x*y=(89y^2/64):(5y^2/8)=89y^2/64*8/5y^2=89/40