Question

Va rog mult! Am mare mare nevoie

Answer 1

$a) \frac{ {4.01 } ^{2} - {0.99}^{2} }{10}$

$= \frac{( \frac{401}{100 } ) ^{2} - {( \frac{99}{100} )}^{2} }{10}$

$= \frac{ \frac{ {401}^{2} }{ {100}^{2} } - \frac{ {99}^{2} }{ {100}^{2} } }{10}$

$= \frac{ \frac{160801}{10000} - \frac{9801}{10000} }{10}$

$= \frac{ \frac{160801 - 9801}{10000} }{10}$

$= \frac{ 151000}{1000}$

$= 151$

$b) \sqrt{5 - 2 \sqrt{6} } \times \sqrt{5 + 2 \sqrt{6} }$

$= \sqrt{(5 - 2 \sqrt{6} )(5 + 2 \sqrt{6} )}$

$= \sqrt{ {5}^{2} - ( {2 \sqrt{6} )}^{2} }$

$= \sqrt{25 - 24}$

$= \sqrt{1}$

$= 1$

$c) \frac{14}{4 \sqrt{2} + 5} + 5 - 8 \sqrt{2}$

$\frac{14}{4 \sqrt{2} + 5} + \frac{5(4 \sqrt{2} + 5)}{4 \sqrt{2} + 5} - \frac{8 \sqrt{2} (4 \sqrt{2} + 5) }{4 \sqrt{2} + 5}$

$= \frac{14 + 20 \sqrt{2} + 25 - 32 \sqrt{4} - 40 \sqrt{2} }{4 \sqrt{2} + 5}$

$= \frac{14 + 20 \sqrt{2} + 25 - 32 \times 2 - 40 \sqrt{2} }{4 \sqrt{2} + 5}$

$= \frac{14 + 20 \sqrt{2} + 25 - 64 - 40 \sqrt{2} }{4 \sqrt{2 }+ 5 }$

$= \frac{ - 25 - 20 \sqrt{2} }{4 \sqrt{2} + 5}$

$= \frac{5( - 5 - 4 \sqrt{2} )}{4 \sqrt{2} + 5}$