Question

xsqure +1/×square =3 fine the value of x-1/×​

Answer 1

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$Answer: \ \bold{\pm 1}$

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$x^2+\frac{1}{x^2}=3 \\ \\ x^2+\frac{1}{x^2}-2=3-2 \\ \\ x^2+\frac{1}{x^2}-(2 \times x \times \frac{1}{x})=1 \\ \\ (x-\frac{1}{x})^2=1 \\ \\ x-\frac{1}{x}=\sqrt{1} \\ \\ x+\frac{1}{x}=\bold{\pm1}$

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$\bold{TO\ REMEMBER...} \\ \\ \\ If \\ \\ x^2+\frac{1}{x^2}=k, \\ \\ then \\ \\ x+\frac{1}{x}=\pm \sqrt{k+2} \\ \\ \& \\ \\ x-\frac{1}{x}=\pm \sqrt{k-2}$

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$Here, \\ \\ x^2+\frac{1}{x^2}=3 \\ \\ \\ k=3 \\ \\ \\ To find :\ x-\frac{1}{x}. \\ \\ So use the second one. \\ \\ \\ \pm\sqrt{k-2} \\ \\ \pm\sqrt{3-2} \\ \\ \pm\sqrt{1} \\ \\ \bold{\pm1}$

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$Thank you. Have a nice day. :-) \\ \\ \\ \#adithyasajeevan$

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