Question

Ajutor. Clasa a VII a. ​

Answer 1

Răspuns:

Explicație pas cu pas:

a) x =+-1, sau +-2

b) x in {-1; 3; 5}

c) x = +-√7

d) √(x^2/2) = x√2/2,  x = +-√2/2

e) x = -√8

f) imposibil

g) imposibil

h)  x = +- √3

Answer 2

$\it -3<x<10\ \ \ \ \ (*)\\ \\ a)\ \ \dfrac{2}{x}\in\mathbb{Z} \ \Rightarrow x\in D_2 \Rightarrow x\in\{-2,\ \ -1,\ \ 1,\ \ 2\},\ care\ verific\breve a\ rela\c{\it t}ia\ (*)\\ \\ \\ b)\ \dfrac{-15}{x}\in\mathbb{Z} \Rightarrow x\in D_{15}\ \stackrel{(*)}{\Longrightarrow}\ x\in\{-1,\ \ 1,\ \ 3,\ \ 5\}$

$\it c)\ \dfrac{2x}{\sqrt7}\in\mathbb{Z} \Rightarrow x=k\sqrt7,\ k\in\mathbb{Z}, \ \stackrel{(*)}{\Longrightarrow}\ x\in\{-\sqrt7,\ \ 0,\ \ \sqrt7,\ \ 2\sqrt7,\ \ 3\sqrt7\}$

$\it d)\ \sqrt{\dfrac{x^2}{2}}\in\mathbb{Z}\ \stackrel{(*)}{\Longrightarrow}\ x\in\{-2\sqrt2,\ \ -\sqrt2, \ 0,\ \sqrt2,\ 2\sqrt2,\ 3\sqrt2,\ 4\sqrt2,\ 5\sqrt2,\ 6,\sqrt3,\ 7\sqrt2\}$