Question

find the answer of this question

Answer 1

Hope u like my process
======================
Given that...

$\alpha \: \: \: and \: \: \: \beta$

are the roots of x² + x + 1 = 0
So,
.
$\alpha = \frac{ - 1 + \sqrt{1 - 4} }{2} = \frac{ - 1 + \sqrt{ - 3} }{2} \\ \beta = \frac{ - 1 - \sqrt{1 - 4} }{2} = \frac{ - 1 + \sqrt{ - 3} }{2}$

Similarly,
.
$\gamma \: \: \: and \: \: \: \sigma$

Are the roots of x² +3x +1 =0
So,

$\gamma = \frac{ - 3 + \sqrt{ {3}^{2} - 4 } }{2} = \frac{ - 3 + \sqrt{5} }{2} \\ \sigma = \frac{ - 3 - \sqrt{ {3}^{2} - 4 } }{2} = \frac{ - 3 - \sqrt{5} }{2}$

Now by problem,
--------------------------
Plz.. Check the image for next step
Hope this is ur required answer
Proud to help you