Question

Numerele x si y sunt invers proportionale cu 6 si, respectiv 5. Calculati valorile rapoartelor :
3x+8y/5x+y ; x^2+y^2/8xy.

Answer 1

Raspuns postat de finamihai ☕ Geniu ☕

la data de  2014-03-27T00:15:44+02:00

{x,y} i.p{6,5}

x·6=y·5=k

6x=k⇒x=k/6

5y=k⇒y=k/5

inlocuim in 3x+8y/5x+y⇒

(3k/6+8k/5)/(5k/6+k/5) aducem la acelasi numitor⇒

(15k/30+48k/30)/(25k/30+6k/30)⇒

63k/30:31k/30⇒63k/30·30/31k⇒63/31

deci valoarea RAPORTULUI ESTE 63/31=2,032....

2. pt.x²+y²/8xy

⇒(k²/36+k²/25)/8·k/6·k/5⇒

(25k²/900+36k²/900)/8k²/30⇒

71k²/900:8k²/30⇒

71k²/900 · 30/8k² ⇒ 71/240

valoarea raportului este 71/240=0.29583