Question

Determinati numerele a,b,c € Q invers proportionale cu nr 4,16,27 stiind ca AxBxB = 1

Answer 1

$4a+16b=27c=k\Rightarrow a=k/4;\ b=k/16;\ c=k/27$

$abc=1\Rightarrow \dfrac k4\cdot\dfrac{k}{16}\cdot\dfrac{k}{27}=1\Rightarrow k^3=4^3\cdot3^3\Rightarrow k=12$  Deci:

$a=3;\ b=\dfrac34; \ c=\dfrac49$