Question

Este urgent!!!Vă rog.​

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

Explicație pas cu pas:

a)

$E(x) = (2x - 1)^{2} - ( x + 1)^{2} - (2x^{2} + 3) = 4 {x}^{2} - 4x + 1 - {x}^{2} - 2x - 1 - 2 {x}^{2} - 3 = 4 {x}^{2} - 3 {x}^{2} - 6x + 1 - 4 = {x}^{2} - 6x - 3$

b)

$E(a) \leqslant 0$

${a}^{2} - 6a - 3 \leqslant 0$

${a}^{2} - 6a - 3 = 0$

$\Delta = 36 + 12 = 48$

$a_{1;2} = \dfrac{ - ( - 6) \pm \sqrt{48} }{2} = \dfrac{6\pm 4\sqrt{3} }{2} = \dfrac{2(3\pm 2\sqrt{3})}{2} = 3\pm 2\sqrt{3}$

$\implies 3 - 2 \sqrt{3} \leqslant a \leqslant 3 + \sqrt{2}$

$\pm \sqrt{3} \approx \pm 1.73... \\ - 1 \leqslant 3 - 2 \sqrt{3} \leqslant 0 \\ 6 \leqslant 3 + 2 \sqrt{3} \leqslant 7$

$\implies a \in \Big\{ 0; 1; 2; 3; 4; 5; 6\Big\}$