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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⇒
(25k²/750+36k²/750)/8k²/30⇒
71k²/750:8k²/30⇒
71k²/750·30/8k²⇒213/400
valoarea raportului este 213/400=0,5425