Question

If x-= √5, find the values of :
(i) Х+1/x , (ii) X2+1/X2 (iii) x3 + 1/x3

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Answer 1

$\huge \fbox \red{answer}$

$i) \: x + \frac{1}{x} = \sqrt{5} + \frac{1}{ \sqrt{5} }$

$= \frac{ \sqrt{5} \times \sqrt{5} }{ \sqrt{5} } + \frac{1}{ \sqrt{5} } = \frac{5 + 1}{5} = \frac{6}{5}$

$ii) \: \frac{x^{2} + 1}{ {x}^{2} } = \frac{ \sqrt{5} \:^{2} +1 }{ \sqrt{5}^{2} } = \frac{5 + 1}{5} = \frac{6}{5}$

$iii) \: {x}^{3} + \frac{1}{{x}^{3} } = \sqrt{5}^{3} + \frac{1}{ \sqrt{5}^{3} }$

$= \frac{5 \sqrt{5} \times 5 \sqrt{5} }{5 \sqrt{5} } + \frac{1}{5 \sqrt{5} }$

$= \frac{25(5) + 1}{25(5)} = \frac{125 + 1}{125} = \frac{126}{125}$

Hope this helps!!❤️