Question

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Answer 1

Step-by-step explanation:

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Answer 2

EXPLANATION.

$\implies \dfrac{4 + \sqrt{2} }{2 + \sqrt{2} } = x - \sqrt{y}$

As we know that,

Rationalizes the equation, we get.

$\implies \dfrac{4 + \sqrt{2} }{2 + \sqrt{2} } \times \dfrac{2 - \sqrt{2} }{2 - \sqrt{2} }$

$\implies \dfrac{(4 + \sqrt{2} )(2 - \sqrt{2} )}{(2 + \sqrt{2} )(2 - \sqrt{2}) }$

$\implies \dfrac{4(2 - \sqrt{2} ) + \sqrt{2} ( 2 - \sqrt{2} )}{(2)^{2} - (\sqrt{2})^{2} }$

$\implies \dfrac{8 - 4\sqrt{2} + 2\sqrt{2} - 2 }{4 - 2}$

$\implies \dfrac{6 - 2\sqrt{2} }{2} = \dfrac{2(3 - \sqrt{2} )}{2} = 3 - \sqrt{2}$

$\implies 3 - \sqrt{2} = x - \sqrt{y}$

$\implies x = 3 \ \ \ \ y = 2$