Question

Determinati multimea
A ={x apartine lui N |x, 2, 6, 9 sunt termenii unei proportii}

Answer 1

A= {3;2;6;9}
9*2=6x
6x=18
x=18:6
x=3
Mai exista si alta solutie:
9*6=2x
2x=54
x=54:2
x=27
Proportia:
$\frac{2}{3}= \frac{6}{9}$
Se pot forma mai multe proportii. Eu am scris una.
S={3;27}

Answer 2

Daca x, 2, 6, 9 sunt termenii unei proportii, atunci putem avea urmatoarele proportii:

$I.~ \frac{x}{2}= \frac{6}{9} \\ II.~ \frac{x}{2}= \frac{9}{6} \\ III.~ \frac{x}{6}= \frac{2}{9} \\ IV.~ \frac{x}{6}= \frac{9}{2} \\ V.~ \frac{x}{9}= \frac{2}{6} \\ VI.~ \frac{x}{9}= \frac{6}{2}$

$I.=\ \textgreater \ x= \frac{2*6}{9}$∉N
$II.=\ \textgreater \ x= \frac{2*9}{6}=3. \\ III.=\ \textgreater \ x= \frac{6*2}{9}$∉N
$IV.=\ \textgreater \ x= \frac{6*9}{2}=27 \\ V.=\ \textgreater \ x= \frac{9*2}{6}=3 \\ VI.=\ \textgreater \ x= \frac{9*6}{2}=27$

Deci x∈{3;27} => A={3;27}.