Question

if a and b are rational numbers then find the value of a and b in
$3 + \sqrt{5} \div 3 - \sqrt{5 = a + b \: \sqrt{7} }$



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Answer 1

$\large\mathbb \pink{\fcolorbox{pink}{black}{ YØUR-ANSWER \ }}$

$On \: Rationalizing \: we \: get,$

$\begin{gathered} \frac{3 + \sqrt{5} }{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } \\ = \frac{ {(3 + \sqrt{5} )}^{2} }{9 - 5} \\ = \frac{9 + 5 + 6 \sqrt{5} }{4} \\ \frac{7 + 3 \sqrt{5} }{2} = a + b \sqrt{5} \end{gathered}$

$On \: comparing \: both \: sides \: we \: get,$

$a = 7/2 and b = 3/2$

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Answer 2

Answer:

3/2 is the correct answer

hope it helps