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

Răspuns :

Fie a,b-nr.

[tex] \frac{a + b}{2} = 9.5 = > a + b = 2 \times 9.5 = 19[/tex]

[tex] \frac{a}{b} = 2.1(6) = \frac{216 - 21}{90} = \frac{205}{90} = \frac{41}{18} [/tex]

[tex] \frac{a}{b} = \frac{41}{18} = > 18a = 41b = > a = \frac{41b}{18} [/tex]

[tex]a + b = 19[/tex]

[tex] \frac{41b}{18} + b = 19 \: | \times 18[/tex]

[tex]41b + 18b = 342[/tex]

[tex]59b = 342[/tex]

[tex]b = \frac{342}{59} [/tex]

[tex]a + b = 19[/tex]

[tex]a = 19 - b[/tex]

[tex]a = 19 - \frac{342}{59} [/tex]

[tex]a = \frac{1121}{59} - \frac{342}{59} [/tex]

[tex]a = \frac{1121 - 342}{59} [/tex]

[tex]a = \frac{779}{59} [/tex]