Question

$3 + \sqrt{5} \div 3 - 2 \sqrt{5}$
a-b√5​

Answer 1

Answer:

$\huge\mathcal{\purple{answer = \frac{7+ \sqrt[3]{5}}{2}}}$

Step-by-step explanation:

By Rationalizing the denominator ;

$</u><u>=</u><u> \frac{3 + \sqrt{5} }{3 - \sqrt{5} }$

$</u><u>=</u><u>\frac{3 + \sqrt{5} }{3 - \sqrt{5} } = \frac{3 + \sqrt{5} }{3 + \sqrt{5} }$

$by \: using \: identity$

${a}^{2} - {b}^{2} = (a - b)(a + b)$

$</u><u>=</u><u> \frac{(3 + \sqrt{5)</u><u>}</u><u>{</u><u>(3 + \sqrt{5)} } }{ {3}^{2} - { \sqrt{5} }^{2} }$

$by \: using \: identity$

${(a + b</u><u>)</u><u>}^{2} = {a}^{2} + {b}^{2} + 2(a)(b)$

$</u><u>=</u><u>\frac{ {3}^{2} + { \sqrt{5} }^{2} </u><u> + 2(3)( \sqrt{5)} }{9 - 5}$

$</u><u>=</u><u>\frac{9 + 5 + \sqrt[6]{5} }{4}$

$</u><u>=</u><u> \frac{14 + \sqrt[6]{5} }{4}$

By taking 2 common,

$= \frac{7 + \sqrt[3]{5} }{2}$

$<marquee> { hope it help you}$