Question

Fie A multimea solutiilor reale de ecuatie 3x la a 2 - 5x-2=0
a) A/Z b) card A reuniune N c) A U acolada -2;2 acolada d)A reuniune paranteza patrata -1;-1/2
va rog urgent!!!!! clasa 9

Answer 1

Răspuns:

Explicație pas cu pas:

3x^2 - 5x - 2 = 0

Δ = 25 + 24 = 49

x1 = (5 + 7)/6 = 12/6 = 2

x2 = (5 - 7)/6 = -2/6 = -1/3

A = {-1/3; 2}

a) A \ Z = {-1/3}

b) nu cred ca se cere cardinalul reuniunii lui A cu N

ar fi ∞

c) A U {-2; 2} = {-2; -1/3; 2}

d) A U [-1; -1/2] = { [-1; -1/2]; 2}

Answer 2

Ecuația $3x^2-5x-2 = 0$ are:

• $\Delta = (-5)^2-4\cdot 3\cdot (-2) = 25+24 = 49$

• $x_{1,2} = \frac{5\pm \sqrt{49}}{2\cdot 3} = \frac{5\pm 7}{6}\Rightarrow \left|\begin{aligned}&x_1 = \frac{5-7}{6} = -\frac{1}{3}\\&x_2 =\frac{5+7}{6}=2 \end{aligned}\right.$

Astfel,

$A = \left\{-\frac{1}{3}; 2\right\}$

Rezolvarea cerințelor:

$a)\,\,\,A$ / $\mathbb{Z}= \left\{-\frac{1}{3}; 2\right\}$ / $\mathbb{Z} = \left\{-\frac{1}{3}\right\}$

$b)\,\,\,\text{card}(A\cap \mathbb{N}) = \text{card}\left(\left\{-\frac{1}{3}; 2\right\}\cap \mathbb{N}\right) = \text{card}\{2\} = 1$

$c)\,\,\,A\cup \left\{-2; 2\right\} = \left\{-\frac{1}{3}; 2\right\}\cup \left\{-2; 2\right\} = \left\{-2;-\frac{1}{3}; 2\right\}$

$d)\,\,\,A \cap \left[-1; -\frac{1}{2}\right] = \left\{-\frac{1}{3}; 2\right\} \cap \left[-1; -\frac{1}{2}\right] = \varnothing$