Question

partea fracționala a numărului
$\frac{7}{5 \sqrt{2} - 1 }$

Answer 1

$\frac{7}{5 \sqrt{2} - 1} = \frac{7(5 \sqrt{2} + 1)}{(5 \sqrt{2} - 1)(5 \sqrt{2} + 1)}$

$= \frac{35 \sqrt{2} + 7 }{( {5 \sqrt{2} )}^{2} - {1}^{2} }$

$= \frac{35 \sqrt{2} + 7}{50 - 1}$

$= \frac{35 \sqrt{2} + 7}{49}$

$= \frac{7(5 \sqrt{2} + 1)}{49}$

$= \frac{5 \sqrt{2} + 1}{7}$

$= \frac{5 \times 1.41 + 1}{7}$

$= \frac{7.05 + 1}{7}$

$= \frac{8.05}{7}$

$= 1.15$

$[1.15 ] = 1$

${1.15} = 1.15 - [1.15 ]$

$= 1.15 - 1$

$= 0.15$