Question

Nu imi iese o problema cu marimi invers proportionale. Uite problema:
x,y,z i.p 0,8; 0,6; 0,4.
a) x+y+z=260
b)2x+3y+4z=245
c)x patrat+y patrat+z patrat(la puterea a doua)=1525
d)1/x+1/y+1/z=0,25.



Va rog sa ma ajutati

Answer 1

{x,y,z} i.p.{0,8; 0,6; 0,4}
0,8=8/10=4/5
0,6=6/10=3/5
0,4=4/10=2/5

4x/5=3y/5=2z/5=k

4x/5=k⇒x=5k/4
3y/5=k⇒y=5k/3
2z/5=k⇒z=5k/2

x+y+z=260 inlocuim x,y,z

5k/4+5k/3+5k/2=260 aducem la acelasi numitor comun, care este 12, amplificam si obtinem

(15k+20k+30k)/12=260

65k=260·12⇒k=260·12/65⇒k=48

x=5k/4=5·48/4⇒x=60

y=5k/3=5·48/3⇒y=80

z=5k/2=5·48/2⇒z=120