( 5+√( 5 ) #160; ) ( 5 √( 5 ) #160; ) =( 25 5 ) #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; ...

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Proof by mathematical induction

Solve : 5+√...

Question

Solve : $(5 + \sqrt{5}) (5 - \sqrt{5})$

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Solution

$(5 + \sqrt{5}) (5 - \sqrt{5})$
$= (25 - 5)$ $(∵ (a + b) (a - b) = a^{2} - b^{2})$
$= 5$

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