Question

5.If X =3—√5,then x²+ 1/x² =?​

Answer 1

Step-by-step explanation:

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Answer 2

$\frac{1}{x}$=$\frac{1}{3-\sqrt{5} }$(rationalize it)

$\frac{1}{x}$=$\frac{3+\sqrt{5} }{2}$

x=3—√5

now find $x^{2}$ and $\frac{1}{x^{2} }$

$x^{2}$=13-6$\sqrt{5}$

$\frac{1}{ x^{2} }$=$\frac{13+6\sqrt{5} }{4}$

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

13-6$\sqrt{5}$+$\frac{13+6\sqrt{5} }{4}$+2

(52-24$\sqrt{5}$+13+6$\sqrt{5}$+8)/4

(73-18$\sqrt{5}$)/4