Question

if x2 + 1\x2 = 3 , find (a) x - 1\x (b) x + 1\x​

Answer 1

Answer:

$x^2+\frac{1}{x^2}=3\\\\x^2+\frac{1}{x^2}=1+2\\\\x^2+\frac{1}{x^2}-2=1\\\\x^2+(\frac{1}{x})^2-2(x)(\frac{1}{x})=1\\\\(x-\frac{1}{x})^2=1^2\\\\x - \frac{1}{x}=1\\\\\frac{x-1}{x}=1$

And,

$x^2+\frac{1}{x^2}=3\\\\x^2+\frac{1}{x^2}=5-2\\\\x^2+\frac{1}{x^2}+2=5\\\\x^2+(\frac{1}{x})^2+2(x)(\frac{1}{x})=5\\\\(x+\frac{1}{x})^2=(\sqrt{5}) ^2\\\\x + \frac{1}{x}=\sqrt{5}\\\\\frac{x+1}{x}=\sqrt{5}$

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Answer 2

1 and $\sqrt5$ respectively