Question

if x + 1/x=2 find the value of x² + 1/x²​

Answer 1

$\underline{ \underline{\large\green\maltese \large{ \bf \red{Given:-}}}}$

$\bull \: \large\sf x + \large{\frac{1}{x}} = 2$

$\underline{ \underline{\large\purple\maltese \large{ \bf \orange{To\: Find:-}}}}$

$\large{ \leadsto} \sf \: Value \: of \: \boxed{ x^2 +\frac{ 1}{ {x}^{2} } }$

$\underline{ \underline{\large\blue\maltese \large{ \bf \green{Solution:-}}}}$

$\large \star \: \sf x+ \frac{1}{x} = 2$

$\underline{\sf{Squaring\:both\:sides}}$

$: \implies$$\sf{(x + \frac{1}{x} )}^2 = (2)^2$

$: \implies$$\sf ((x)^2 +{(\frac{1}{x})}^2+2(\cancel{x})(\frac{1}{\cancel{x}})) = 4$

$\quad\quad\quad\quad\quad\quad\quad\sf((a+b)^2=a^2+b^2+2ab)$

$: \implies$$\sf (x^2 +\frac{1}{x^2})+2= 4$

$: \implies$$\sf (x^2 +\frac{1}{x^2})= 4-2$

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

Answer 2

Answer:

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