Question

Va rog ex 2! Dau 50 puncte!

Answer 1

Explicație pas cu pas:

$a = 2 \sqrt{6} \bigg(\dfrac{3}{ \sqrt{2} } - \dfrac{5}{ \sqrt{3} }\bigg) + \dfrac{18}{3 \sqrt{2} + 2 \sqrt{3} } =$

$= \dfrac{6 \sqrt{6} }{ \sqrt{2} } - \dfrac{10 \sqrt{6} }{ \sqrt{3} } + \dfrac{18(3 \sqrt{2} - 2 \sqrt{3})}{(3 \sqrt{2} + 2 \sqrt{3})(3 \sqrt{2} - 2 \sqrt{3})}$

$= 6 \sqrt{3} - 10 \sqrt{2} + \dfrac{18(3 \sqrt{2} - 2 \sqrt{3})}{ {(3 \sqrt{2})}^{2} - {(2 \sqrt{3} )}^{2} }$

$= 6 \sqrt{3} - 10 \sqrt{2} + \dfrac{18(3 \sqrt{2} - 2 \sqrt{3})}{18 - 12}$

$= 6 \sqrt{3} - 10 \sqrt{2} + \dfrac{18(3 \sqrt{2} - 2 \sqrt{3})}{6}$

$= 6 \sqrt{3} - 10 \sqrt{2} + 3(3 \sqrt{2} - 2 \sqrt{3})$

$= 6 \sqrt{3} - 10 \sqrt{2} + 9 \sqrt{2} - 6 \sqrt{3})$

$= - \sqrt{2}$

.

$b = \dfrac{10}{4 \sqrt{2} + 3 \sqrt{3} } - 3 |2 \sqrt{3} - 3 \sqrt{2} | + 1 =$

$= \dfrac{10(4 \sqrt{2} - 3 \sqrt{3})}{(4 \sqrt{2} + 3 \sqrt{3})(4 \sqrt{2} - 3 \sqrt{3}) } - 3 (3 \sqrt{2} - 2 \sqrt{3}) + 1$

$= \dfrac{10(4 \sqrt{2} - 3 \sqrt{3})}{ {(4 \sqrt{2})}^{2} - {(3 \sqrt{3})}^{2} } - 9 \sqrt{2} + 6 \sqrt{3} + 1$

$= \dfrac{10(4 \sqrt{2} - 3 \sqrt{3})}{ 32 - 27} - 9 \sqrt{2} + 6 \sqrt{3}) + 1$

$= \dfrac{10(4 \sqrt{2} - 3 \sqrt{3})}{5} - 9 \sqrt{2} + 6 \sqrt{3} + 1$

$= 2(4 \sqrt{2} - 3 \sqrt{3}) - 9 \sqrt{2} + 6 \sqrt{3} + 1$

$= 8 \sqrt{2} - 6 \sqrt{3} - 9 \sqrt{2} + 6 \sqrt{3} + 1$

$= 1 - \sqrt{2}$