Question

determinati 2 numere stiind ca media lor aritmetica este 9.5 si raportul lor este 2.1(6).​

Answer 1

Fie a,b-nr.

$\frac{a + b}{2} = 9.5 = > a + b = 2 \times 9.5 = 19$

$\frac{a}{b} = 2.1(6) = \frac{216 - 21}{90} = \frac{205}{90} = \frac{41}{18}$

$\frac{a}{b} = \frac{41}{18} = > 18a = 41b = > a = \frac{41b}{18}$

$a + b = 19$

$\frac{41b}{18} + b = 19 \: | \times 18$

$41b + 18b = 342$

$59b = 342$

$b = \frac{342}{59}$

$a + b = 19$

$a = 19 - b$

$a = 19 - \frac{342}{59}$

$a = \frac{1121}{59} - \frac{342}{59}$

$a = \frac{1121 - 342}{59}$

$a = \frac{779}{59}$