Question

ajutor , puteti sa rezolvati exercitiile de mai jos ? va rog​

Answer 1

Explicație pas cu pas:

1.

$3{(2x + 3 \sqrt{3} )}^{2} - 79 = 146 \\3{(2x + 3 \sqrt{3} )}^{2} = 146 + 79$

$3{(2x + 3 \sqrt{3} )}^{2} = 225 \iff {(2x + 3 \sqrt{3} )}^{2} = 75$

$\implies |2x + 3 \sqrt{3}| = 5 \sqrt{3}$

$2x + 3 \sqrt{3} = - 5 \sqrt{3} \iff 2x = - 5 \sqrt{3} - 3 \sqrt{3}$

$2x = - 8 \sqrt{3} \implies \bf x = - 4 \sqrt{3}$

$2x + 3 \sqrt{3} = 5 \sqrt{3} \iff 2x = 5 \sqrt{3} - 3 \sqrt{3}$

$2x = 2 \sqrt{3} \implies \bf x = \sqrt{3}$

2.

$12 {(x + 1)}^{2} = {(6 + 2 \sqrt{3} )}^{2} \iff {(x + 1)}^{2} = \dfrac{{(6 + 2 \sqrt{3} )}^{2} }{12}$

$\dfrac{{(6 + 2 \sqrt{3} )}^{2} }{12} = {\bigg(\dfrac{2(3 + \sqrt{3})}{2 \sqrt{3} } \bigg)}^{2} = {\bigg(\dfrac{(3 + \sqrt{3}) \sqrt{3} }{3} \bigg)}^{2} = {\bigg(\dfrac{3( \sqrt{3} + 1)}{3} \bigg)}^{2} = {(\sqrt{3} + 1)}^{2}$

${(x + 1)}^{2} = {(\sqrt{3} + 1)}^{2}$

$\implies |x + 1| = \sqrt{3} + 1$

$x + 1 = - \sqrt{3} - 1 \implies \bf x = - \sqrt{3} - 2$

$x + 1 = \sqrt{3} + 1 \implies \bf x = \sqrt{3}$