Question

Hi, anyone able to help with qn 7? Thanks :)!

Answer 1

Answer:

 

Step-by-step explanation:

I used the quadratic formula to find the roots of $x^{2} + x -1$

$a=\frac{-1-\sqrt{5}}{2} b=\frac{-1+\sqrt{5} }{2}$

$\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} )^{2} * \frac{-1+\sqrt{5}}{2}$

$\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} ) * \frac{-1+\sqrt{5}}{2}*(\frac{-1-\sqrt{5}}{2} )$

$\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} ) * \frac{-1+\sqrt{5}-\sqrt{5} -4}{4}$

$\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} ) * \frac{ -4}{4}$

$\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} ) * -1$

$\frac{-1-1\sqrt{5} }{2\sqrt{3} }*-1$

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