Question

va rog frumos dau coroana ​

Answer 1

3) c)

$\boxed {(a - b)(a + b) = {a}^{2} - {b}^{2}}$

$m_{g} = \sqrt{(3 \sqrt{2} - 4)(3 \sqrt{2} + 4)} = \sqrt{{(3 \sqrt{2})}^{2} - {4}^{2}} = \sqrt{18 - 16} = \bf \sqrt{2}$

4) c)

$\boxed {(a \pm b)^{2} = {a}^{2} \pm 2ab + {b}^{2}}$

$\bigg(x + \dfrac{1}{x} \bigg)^{2} = {x}^{2} + 2 \cdot x \cdot \dfrac{1}{x} + \dfrac{1}{ {x}^{2}} = {x}^{2} + 2 + \dfrac{1}{ {x}^{2}}$

${5}^{2} = {x}^{2} + 2 + \dfrac{1}{ {x}^{2}} \implies$

${x}^{2} + \dfrac{1}{ {x}^{2}} = 25 - 2 = \bf 23$

5) d)

$\sqrt{49} < \sqrt{50} < \sqrt{64}$

$\implies 7 < \sqrt{50} < 8$

numerele prime din intervalul [0;√50] sunt:

2; 3; 5; 7

$S = 2 + 3 + 5 + 7 = \bf 17$