Question

ajutor!
1. calculati :
(radical din 3 + radical din 2) totul la puterea -2
2. stiind ca
$\frac{x + 1}{x} = 3 \sqrt{2}$
aflati :
$\frac{ {x }^{2} + 1 }{x {}^{2} } =$
si 3 din imagine (puteti sa imi faceti macar 2 si 3 ?va rog )

Answer 1

Am atasat rezolvarea!

Answer 2

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

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

$= \frac{1}{3 + 2 \sqrt{6} + 2}$

$= \frac{1}{5 + 2 \sqrt{6} }$

$2) \frac{x + 1}{x} = \frac{3}{2}$

$2(x + 1) = 3x$

$2x + 2 = 3x$

$2x - 3x = - 2$

$- x = - 2 \: | \times ( - 1)$

$x = 2$

$\frac{ {x}^{2} + 1}{ {x}^{2} } = \frac{ {2}^{2} + 1}{ {2}^{2} } = \frac{4 + 1}{4} = \frac{5}{4}$

$3) \frac{x - 1}{x} = 5 \sqrt{2}$

$5 \sqrt{2} x = x - 1 \: |( \: )^{2}$

${(5 \sqrt{2} x)}^{2} = {(x - 1)}^{2}$

${50x}^{2} = {x}^{2} - 2x + 1$

$50 {x}^{2} - {x}^{2} + 2x - 1 = 0$

$49 {x}^{2} + 2x - 1 = 0$

$a = 49$

$b = 2$

$c = - 1$

$\Delta = {b}^{2} - 4ac$

$\Delta = {2}^{2} - 4 \times 49 \times ( - 1)$

$\Delta = 4 + 196$

$\Delta = 200$

$x_{1,2} = \frac{ - b\pm \sqrt{\Delta} }{2a}$

$x_{1,2} = \frac{ - 2 \pm \sqrt{200}}{2 \times 49}$

$x_{1,2}= \frac{ - 2\pm10 \sqrt{2} }{98}$

$x_{1}= \frac{ - 2 + 10 \sqrt{2} }{98}$

$x_{1} = \frac{2( - 1 + 5 \sqrt{2} )}{98}$

$x_{1} = \frac{ - 1 + 5 \sqrt{2} }{49}$

$x_{2} = \frac{ - 2 - 10 \sqrt{2} }{98}$

$x_{2} = \frac{2( - 1 - 5 \sqrt{2} )}{98}$

$x_{2} = \frac{ - 1 - 5 \sqrt{2} }{49}$