Răspuns :

102533id

Răspuns:

240 si 320

Explicație pas cu pas:

a + b = 4  ; a,b ≠ 0  ; a,b ∈ N

A = 240 : a + 240 : b

a = 1  ; b = 3 => A = 240:1 + 240:3 = 240+80 = 320

a = 2 ; b = 2 => A = 240:2 + 240:2 = 120+120 = 240

a = 3 ; b = 1 => A = 240:3 + 240:1 = 80+240 = 320

Targoviste44id

[tex]\it Fie \ a,\ b\in\mathbb{N}^*,\ \ a+b=4\ \ \ \ (1)\\ \\ a+b=4 \Rightarrow (a,\ b)\in\{(1,\ 3),\ (2,\ 2),\ (3,\ 1)\} \Rightarrow ab\in\{3,\ \ 4\}\ \ \ \ (2)[/tex]

[tex]\it A=\dfrac{240}{a}+\dfrac{240}{b}=240\Big(\dfrac{1}{a}+\dfrac{1}{b}\Big)=\dfrac{240(a+b)}{ab}\ \stackrel{(1)}{=}\ \dfrac{240\cdot4}{ab}\ \ \ \ \ (3)\\ \\ \\ (2),\ (3) \Rightarrow A\in\Big\{\dfrac{240\cdot4}{3},\ \ \dfrac{240\cdot4}{4}\Big\} \Rightarrow A\in\{320,\ \ 240\}[/tex]

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