Question

Factorise (x+1/x) ^2 +6(x+1/x) +9

Answer 1

Let

$x + \frac{1}{x} \: \: be \: \: y.$

Then,

$\: \: \: \: \: {(x + \frac{1}{x}) }^{2} + 6(x + \frac{1}{x}) + 9 = 0\\ = > {y}^{2} + 6y + 9 = 0 \\ = > {y}^{2} + 3y + 3y + 9 = 0 \\ = > y(y + 3) + 3(y + 3) = 0 \\ = > (y + 3) (y + 3)= 0 \\ = > y = ( - 3)$

$= > x + \frac{1}{x} = ( - 3) \\ = > {x}^{2} + 1 = - 3x \\ = > {x}^{2} + 3x + 1 = 0$

After solving this,

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

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Answer 2

Step-by-step explanation:

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