Question

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7 +375 7-35
3+ V5 3-15
Please tell this-​

Answer 1

$\large\bf\underline\red{Question \: :- }$

$\bigstar \sf \: { \frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} } }$

$\large\bf\underline\red{Answer \: :- }$

Using Formula for multiplication

$\bigstar\sf\pink {(a+b)(a-b) = a²-b²}$

$\small\longmapsto\sf { \frac{(7 + 3 \sqrt{5})(3 - \sqrt{5} ) - (3 + \sqrt{5} )(7 - 3 \sqrt{5}) }{(3 + \sqrt{5})(3 - \sqrt{5} )} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \small\longmapsto\sf{ \frac{7( 3 - \sqrt{5} ) + 3 \sqrt{5}(3 - \sqrt{5}) - (3 + \sqrt{5} )(7 - 3 \sqrt{5} ) }{(3) {}^{2} - ( \sqrt{5}) {}^{2} } } \\ \\ \small\longmapsto\sf{ \frac{21 - 7 \sqrt{5} + 9 \sqrt{15 } - 3( - 5) - (3 + \sqrt{5})(7 - 3 \sqrt{5}) }{9 - 5} } \\ \\ \small\longmapsto\sf{by \: multiplication} \\ \\ \small\longmapsto\sf{ \frac{20 - 7 \sqrt{5} + 9 \sqrt{15} + 15 - 21 + 7 \sqrt{5} - 9 \sqrt{15} - 15}{4} } \\ \\ \small\longmapsto\sf{ \frac{1}{4} } \: \: \: \: (because \: + and - will \: be \: canceled \: ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \small\longmapsto\sf \pink{ \frac{1}{4} }$

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