Question

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Answer 1

Given:-

=> p² = 5p - 3

=> q² = 5q - 3
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» So the equation is x²-5x+3 = 0 have roots p and q
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So,

$= > p = \frac{5 + \sqrt{3} }{2} \\ \\ = > q = \frac{5 - \sqrt{3} }{2}$
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» If a equations have p/q and q/p as root then

As

$= > \frac{p}{q} = \frac{5 + \sqrt{3} }{5 - \sqrt{3} } \\ \\ and \\ \\ = > \frac{q}{p} = \frac{5 - \sqrt{3} }{5 + \sqrt{3} }$
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So,

$= > (x - \frac{5 + \sqrt{3} }{5 - \sqrt{3} } )(x - \frac{5 - \sqrt{3} }{5 + \sqrt{3} } ) = 0 \\ \\ = > {x}^{2} + 1 - x( \frac{5 + \sqrt{3} }{5 - \sqrt{3} } + \frac{5 - \sqrt{3} }{5 + \sqrt{3} } ) = 0 \\ \\ = > {x }^{2} + 1 - x( \frac{76}{12} ) = 0 \\ \\ = > 12 {x }^{2} + 12 - 76x = 0 \\ \\ = > 3 {x}^{2} + 3 - 19x = 0 \\ \\ = > 3 {x}^{2} - 19x + 3 = 0$
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Hence the final equation is "3x²-19x+3 = 0"