Question

c)Determinati x € Z astfel incat x/2 >20/x>x/1,7.
Va rog ajutatima.

Answer 1

x/2 >20/x>x/1,7

[tex]\it\ I)\  \dfrac{x}{2}\ \textgreater \ \dfrac{x}{1,7} \Rightarrow \dfrac{x}{2}-\dfrac{^{10)}x}{\ 1,7} \ \textgreater \ 0 \Rightarrow\dfrac{x}{2}-\dfrac{10x}{17} \ \textgreater \ 0 \Rightarrow \dfrac{17x-20x}{34}\ \textgreater \ 0 \Rightarrow \\\;\\ \\\;\\ \Rightarrow \dfrac{-3x}{34} \ \textgreater \ 0 \Rightarrow -3x\ \textgreater \ 0 |_{\cdot (-1)} \Rightarrow 3x\ \textless \ 0 \Rightarrow x\ \textless \ 0\ \ \ \ (1)[/tex]

$\it \ II)\ \dfrac{x}{2}\ \textgreater \ \dfrac{20}{x}|_{\cdot(-1)} \Rightarrow \dfrac{-x}{2}\ \textless \ \dfrac{20}{-x} \Rightarrow x^2 \ \textless \ 40 \ \ \ \ \ (2)$

[tex]\it\ III)\ \dfrac{20}{x} \ \textgreater \ \dfrac{x}{1,7}|_{\cdot(-1)} \Rightarrow \dfrac{20}{-x} \ \textless \ \dfrac{-x}{1,7}|_{\cdot(-1)} \Rightarrow 20\cdot1,7\ \textless \ (-x)\cdot(-x) \Rightarrow \\\;\\ \\\;\\ \Rightarrow 34\ \textless \ x^2 \Rightarrow x^2\ \textgreater \ 34 \ \ \ \ (3)[/tex]

$\it (2),\ (3) \Rightarrow 34\ \textless \ x^2\ \textless \ 40 \stackrel{(1)}\Longrightarrow} x=-6.$

Answer 2

Scuze , am luat-o mai batraneste , ca la clasa a 9-a, cu semnul expresiei; dar mi-a dat aceeasi solutie ca lui Viorrell