Question

Show that
$(5 + \sqrt{5} ) (5 - \sqrt{5})$
is a rational no.

Answer 1

$(5 + \sqrt{5} )(5 - \sqrt{5} ) \\( a + b)(a - b) = {a}^{2} - {b}^{2} \\ {5}^{2} - { \sqrt[2]{5} }^{2} \\ 25 - 5 \\ 20 \\ hence \: 20 \: is \: a \: rational \: number$
it's your answer

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