Question

Fie proportiile : b\3=2\a și 2\a=3\a+c . Calculați bc .

Answer 1

$\frac{b}{3} = \frac{2}{a}$
$\frac{2}{a} = \frac{3}{a + c}$
$\frac{b}{3} = \frac{2}{a} = > a = \frac{3 \times 2}{b} = \frac{6}{b}$


$\frac{2}{a} = \frac{3}{a + c}$

$\frac{2}{ \frac{6}{b} } = \frac{3}{ \frac{6}{b} + c }$


$\frac{b}{3} = \frac{3}{ \frac{6 + bc}{b} }$


$b \times \frac{6 + bc}{b} = 3 \times 3$


$6 + bc = 9$

$= > bc = 9 - 6 = 3$

$= > bc = 3$