Question

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Answer 1

Explicație pas cu pas:

a)

$x = \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{2} } + \frac{ \sqrt{14} - \sqrt{10} }{2} + \frac{4 \sqrt{3} - 2 \sqrt{7} }{2 \sqrt{2} } = \frac{2 \sqrt{5} - 2 \sqrt{3} + \sqrt{28} - \sqrt{20} + 4 \sqrt{3} - 2 \sqrt{7} }{2 \sqrt{2} } = \frac{2 \sqrt{5} - 2 \sqrt{3} + 2 \sqrt{7} - 2 \sqrt{5} + 4 \sqrt{3} - 2 \sqrt{7} }{2 \sqrt{2} } = \frac{2 \sqrt{3} }{2 \sqrt{2} } = \frac{ \sqrt{3} }{ \sqrt{2} } = \sqrt{ \frac{3}{2} }$

b)

$y = ( \frac{3}{9} + \frac{2}{3} + \sqrt{2} ) \times ( \sqrt{2} - 1) = ( \frac{1}{3} + \frac{2}{3} + \sqrt{2} ) \times ( \sqrt{2} - 1) = ( \frac{1 + 2 + 3 \sqrt{2} }{3} ) \times ( \sqrt{2} - 1) = ( \frac{3 + 3 \sqrt{2} }{3} )( \sqrt{2} - 1) = ( \frac{3(1 + \sqrt{2}) }{3} )( \sqrt{2} - 1) = (1 + \sqrt{2} )( \sqrt{2} - 1) = \sqrt{2 } - 1 + 2 - \sqrt{2} = 1$

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