Question

12. if r²+1/r² =7 evaluate i . r+1/r and ii. r-1/r

answers are given
solve with the process​

Answer 1

${r}^{2} + \frac{1}{ {r}^{2} } = 7 \\ \implies {r}^{2} + \frac{1}{ {r}^{2} } + 2 = 9 \: \: (adding \: 2 \: both \: sides) \\ \implies ( {r + \frac{1}{r} })^{2} = 9...(1) \\ \implies \: r + \frac{1}{r} = ±3 \\ \\ from \: (1) \implies \\ ( {r + \frac{1}{r} })^{2} = 9 \\ \implies \: ( {r - \frac{1}{r} })^{2} + 4 = 9 \\ \implies \: ( {r - \frac{1}{r} })^{2} = 5 \\ \implies \: r - \frac{1}{r} = ± \sqrt{5}$