Question

answer urgently

if you can​

Answer 1

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \red{ \: \: SOLUTION \: \: } \mid}}}}}$

$\: \underline{ \bold{ \: \: Given \: :} } \: \: \: \: \: \: \: \: \bold{p + \frac{1}{p} = 3} \\ \\ \\ \underline{ \bold{ \:To \: \: find \: : }} \: \: \: \: \bold{(i) \: \: p {}^{2} + \frac{1}{p {}^{2} } } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{(ii) \: \: p - \frac{1}{p} }$

$\bold{(i)} \\ \\ \: \: \: \: \: \: \: \: \bold{p + \frac{1}{p} = 3 } \\ \\ \bold{ = > (p + \frac{1}{p}) {}^{2} = (3) {}^{2} } \\ \\ \bold{ = > p {}^{2} + ( \frac{1}{p}) {}^{2} + 2.p. \frac{1}{p} = 9 } \\ \\ \bold{ = > p {}^{2} + \frac{1}{p {}^{2} } + 2 = 9} \\ \\ \bold{ = > p {}^{2} + \frac{1}{p {}^{2} } = 9 - 2 } \\ \\ \bold{ \therefore \: \: \: \underline{ \: \: p {}^{2} + \frac{1}{p {}^{2} } = 7 \: \: \: }}$

$\bold{(ii)} \\ \: \: \: \: \: \: \: \: \underline{ \bold{ \: \: We \: \: have</p><p> \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \bold{p {}^{2} + \frac{1}{p {}^{2} } = 7} \\ \\ \bold{ = > p {}^{2} + \frac{1}{p {}^{2} } - 2 + 2 = 7 } \\ \\ \bold{ = > (p - \frac{1}{p}) {}^{2} - 2 = 7 } \\ \\ \bold{ = > (p - \frac{1}{p}) {}^{2} = 7 + 2 } \\ \\ \bold{ = > (p - \frac{1}{p}) {}^{2} = 9 } \\ \\ \bold{ = > p - \frac{1}{p}= \sqrt{9} } \\ \\ \bold{ \therefore \: \: \: \underline{ \: \: p - \frac{1}{p}= 3 \: \: }}$