Question

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Answer 1

(x+1/x)^2=8^2

x^2+1/x^2+2=64

x^2+1/x^2=64-2=62

(a-1/a)^2=5^2

a^2+1/a^2-2=25

a^2+1/a^2=25+2=27


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Answer 2

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$<b>Solution:$

$\bold{x + \frac{1}{x} = 8} \\ \\ \bold{squaring \: both \: sides} \\ \\ \bold{(x + \frac{1}{x}) {}^{2} = (8) {}^{2} } \\ \\ \bold{x {}^{2} + \frac{1}{x {}^{2} } + 2 \times \cancel {x }\times \frac{1}{ \cancel{x}} = 64 } \\ \\ \bold{x {}^{2} + \frac{1}{x {}^{2} } + 2 = 64 } \\ \\ \bold{x {}^{2} + \frac{1}{x {}^{2}} = 64 - 2} \\ \\ \bold{x {}^{2} + \frac{1}{x {}^{2}} = 62}$

2)

$\bold{a - \frac{1}{a} = 5 } \\ \\ \bold{squaring \: both \: sides} \\ \\ \bold{(a - \frac{1}{a}) {}^{2} = (5) {}^{2} } \\ \\ \bold{a {}^{2} + \frac{1}{a {}^{2} } - 2 = 25} \\ \\ \bold{a {}^{2} + \frac{1}{a {}^{2} } = 25 + 2 } \\ \\ \bold{a {}^{2} + \frac{1}{a {}^{2} } = 27}$


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