Question

If x² - 3x - 1=0, find the value of x²+1/x²
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Answer 1

Answer:

$\huge\sf\blue{\underline{\underline{\purple{Answer}}}}$

but by finding it's roots of x we get that x>1 so ,

=x-1/x>0

=x^2–1/x^2=3√5

Answer 2

Given :-

x² - 3x + 1 = 0

Find :-

x² + 1/x²

Solution :-

x² - 3x + 1 = 0

= x² + 1 = 3x

$\mathbf{ \frac{{x}^{2}}{x} + \frac{1}{x} = \frac{3x}{x} }$

[Dividing Both Sides By X]

$\mathbf{ x + \frac{1}{x} = 3 }$

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

$\mathbf{ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 9}$

$\mathbf{ {x}^{2} + \frac{1}{ {x}^{2} } = 9 - 2}$

$\mathbf{ {x}^{2} + \frac{1}{ {x}^{2} } = 7}$