Question

aflati m;p;q stiind ca sunt invers proportionale cu 2/3;4/5;8/9 si ca m patrat+p patrat+ q patrat= 325/576


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Answer 1

{m;p;q} invers proportionale cu {2/3;4/5;8/9 };m²+p²+ q²= 325/576

2m/3=4p/5=8q/9=k

m=3k/2; p=5k/4; q=9k/8

9k²/4+25k²/16+81k²/64=325/256  ;  aducem la acelasi numitor  (256)

576k²+400k²+324k²=325

1300k²=325   /:325

4k²=1 => k²=1/4 => k=+/- 1/2

m=+/- 3/4 ; p=+/- 5/8; q=+/- 9/16

(m;p;q)={(-3/4; -5/8; -9/16); (3/4; 5/8; 9/16)}