Question

Determinati numerele a,b,c stiind ca a si b sunt d.p cu 5 si 8,b si c sunt invers proportionale cu 3 si2 ,iar 3a+2b-c=57. Va rog dau coroana.​

Answer 1

 

$\displaystyle\bf\\\frac{a}{5}=\frac{b}{8}=k\\\\\boxed{\bf~a=5k}\\\boxed{\bf~b=8k}\\----\\3b=2c\\b=8k\\3\times8k=2c\\24k=2c\\\\c=\frac{24k}{2}\\\\\boxed{\bf~c=12k}\\\\---\\3a+2b-c=57\\3\times5k+2\times8k-12k=57\\15k+16k-12k=57\\19k=57\\\\k=\frac{57}{19}\\\\\boxed{\bf~k=3}\\\\\\a=5k\\\boxed{\bf~a=15}\\b=8k\\\boxed{\bf~b=24}\\c=12k\\\boxed{\bf~c=36}$