Question

Daca x supra y = 2 supra 3, calculati 3x+2y supra x+3y. As dori rezolvarea completă. Merci anticipat.

Answer 1

Se aplica formula:
a/b=c/d
ad=bc
Modul 1:
x/y=2/3
3x=2y
x=2k
y=3k
3x+2y=2k*3+3k*2=6k+6k=12k
x+3y=2k+3k*3=2k+9k=11k
(3x+2y)/(x+3y)=(12k)/(11k)=12/11
Modul 2:
x/y=2/3
3x=2y
x=2y/3
3x+2y=2y/3*3+2y=6y/3+2y=2y+2y=4y
x+3y=2y/3+3y=2y/3+9y/3=(2y+9y)/3=11y/3
(3x+2y)/(x+3y)=(4y)/(11y/3)=(4y*3)/(11y)=(12y)/(11y)=12/11
Modul 3:
x/y=2/3
3x=2y
y=3x/2
3x+2y=3x+3x/2*2=3x+6x/2=3x+3x=6x
x+3y=x+3x/2*3=x+9x/2=2x/2+9x/2=(2x+9x)/2=11x/2
(3x+2y)/(x+3y)=(6x)/(11x/2)=(6x*2)/(11x)=(12x)/(11x)=12/11