Question

if x+ root 10 y = root 5+ root 2 /root 5 - root 2.find x and y​

Answer 1

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$x + \sqrt{10} y = \frac{ \sqrt{5} + \sqrt{2}}{ \sqrt{5} - \sqrt{2}}$

$\implies x + \sqrt{10} y = \frac{ (\sqrt{5} + \sqrt{2} )( \sqrt{5} + \sqrt{2} )}{( \sqrt{5} - \sqrt{2} )( \sqrt{5} + \sqrt{2} )}$

$\implies x + \sqrt{10} y = \frac{5 + 2 + 2 \sqrt{10} }{5 - 4}$

$\implies x + \sqrt{10} y = \frac{7 + 2 \sqrt{10} }{1}$

$\implies x + \sqrt{10} y = 7 + 2 \sqrt{10}$

$\implies x = 7$

$\implies y = 2$

Therefore, x=7, y=2.

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