Question

Simplify (7+√5)/7- (√5)+(7-√5)/(7+√5)​

Answer 1

$\frac{(7+\sqrt{5})}{(7-\sqrt{5})} + \frac{(7-\sqrt{5})}{(7+\sqrt{5})}$

$= \frac{ (7+\sqrt{5})^{2} + (7-\sqrt{5})^{2} }{ (7+\sqrt{5})(7-\sqrt{5})}$

$= \frac{ 2[ 7^{2} +( \sqrt{5})^{2} }{7^{2} - (\sqrt{5})^{2}}$

$= \frac{2( 49 + 5 )}{49-5}$

$= \frac{2\times 54 }{ 44}$

$= \frac{54}{22}$

$= \frac{27}{11}$

Therefore.,

$\red{\frac{(7+\sqrt{5})}{(7-\sqrt{5})} + \frac{(7-\sqrt{5})}{(7+\sqrt{5})}}$

$\green {= \frac{27}{11}}$

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