Question

$(√3-√5) (√5+√3) / (7-2√5)$


simplify it.


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Answer 1

$\sf \colorbox{skyblue} {Question:–}$

$\frac{( \sqrt{3} - \sqrt{5} )( \sqrt{5} + \sqrt{3} )}{7 - 2 \sqrt{5} }$

$\sf \colorbox{lightgreen} {Answer:–}$

$⇒ \frac{( \sqrt{3} - \sqrt{5} )( \sqrt{5} + \sqrt{3} )}{7 - 2 \sqrt{5} }$

$⇒ \frac{( - 5 + 3)}{(7 - 2 \sqrt{5} )} \: \[ \left[ {a}^{2} - {b}^{2} = (a + b)(a - b)\right] \]$

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

$⇒ \frac{ - 14 - 4 \sqrt{5} }{49 - 20}$

$= \frac{ - 1}{29} (14 + 4 \sqrt{5})$

$\\ \\ \\ \\ \\ \\ \sf \colorbox{gold} {\red(ANSWER ᵇʸ ⁿᵃʷᵃᵇ⁰⁰⁰⁸}$