Question

stabiliti daca numarul a=( radical din 2/ 3 - radical din 5) totul la puterea a doua - radical din 180( 1 - radical din 2/ radical din 2 + radical din 2 - radical din 3/ radical din 6 + radical din 3 - radical din 4/ radical din 12) este numar natural.

"/" reprezinta fractie

Answer 1

Explicație pas cu pas:

$a = ( \frac{ \sqrt{2} }{ \sqrt{3} } - \sqrt{5} )^{2} - \sqrt{180} (1 -$

$- 1 + \sqrt{2} - \frac{ \sqrt{18} }{6} + \sqrt{3} - \frac{ \sqrt{48} }{12}) =$

$= ( \frac{2}{3} - \frac{2 \sqrt{10} }{ \sqrt{3} } + 5) - 6 \sqrt{5} ( \sqrt{2} -$

$- \frac{3 \sqrt{2} }{6} + \sqrt{3} - \frac{4 \sqrt{3} }{12}) = ( \frac{2}{3} - \frac{2 \sqrt{30} }{3} +$

$+ \frac{5}{3} ) - 6 \sqrt{5} ( \frac{12 \sqrt{2} }{12} - \frac{6 \sqrt{2} }{12} + \frac{12 \sqrt{3} }{12} ) -$

$- \frac{4 \sqrt{3} }{12} ) = ( \frac{7}{3} - \frac{2 \sqrt{3} }{3} ) - 6 \sqrt{5} ( \frac{6 \sqrt{2} }{12} +$

$+ \frac{12 \sqrt{3} }{12} - \frac{4 \sqrt{3} }{12} ) = ( \frac{7}{3} - \frac{2 \sqrt{3} }{3} ) -$

$- (\frac{36 \sqrt{10} }{12} + \frac{72 \sqrt{15} }{12} - \frac{24 \sqrt{15} }{12} ) =$

$= \frac{7}{3} - \frac{2 \sqrt{3} }{3} - \frac{36 \sqrt{10} }{12} - \frac{72 \sqrt{15} }{12} +$

$+ \frac{24 \sqrt{15} }{12} = \frac{7}{3} - \frac{2 \sqrt{3} }{3} - \frac{9 \sqrt{10} }{3} -$

$- \frac{18 \sqrt{15} }{3} + \frac{6 \sqrt{15} }{3} = \frac{7}{3} - \frac{2 \sqrt{3} }{3} -$

$\frac{9 \sqrt{10} }{3} - \frac{12 \sqrt{15} }{3}$

Cred că exercițiul nu este corect.