Question

$simplify \\ 7 + 3 \sqrt{5} \div 3 + \sqrt{5 } + 7 - 3 \sqrt{5} \div 3 - \sqrt{5}$
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Answer 1

Answer:

Ans: 3

Step-by-step explanation:

$Let \ Z=(7+3\sqrt{5} )\div (3+\sqrt{5} ) +(7-3\sqrt{5} ) \div (3-\sqrt{5})\\\\=\frac{7+3\sqrt{5} }{3+\sqrt{5} } + \frac{7-3\sqrt{5} }{3-\sqrt{5} }\\\\\\Now \ LCM \ of \ 3+\sqrt5 \ and \ 3-\sqrt5\\\\=(3+\sqrt5 )( 3-\sqrt5)=9-5=4\\\\Thus\\\\Z=\frac14 [ (7+3\sqrt5)(3-\sqrt5) + (7-3\sqrt5)(3+\sqrt5) ]\\\\=\frac14 [ 21-7\sqrt5+9\sqrt5-15) + (21+7\sqrt5-9\sqrt5-15]\\\\=\frac14 [6+2\sqrt5+6-2\sqrt5]\\\\=\frac14( 12)\\\\=\frac{12}{4}\\\\=3$