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Answer:
1/x = (1+√5)/2 ≈ 1.618034
Step-by-step explanation:
Since you are only interested in the second part, we presume you have solved the quadratic equation to find ...
x = (√5 -1)/2 ≈ 0.618034
The second part asks for 1/x. The usual method for rationalizing the denominator will be useful for this. Multiply numerator and denominator by the conjugate of the denominator.
[tex]\dfrac{1}{x}=1\div\dfrac{\sqrt{5}-1}{2}=1\times\dfrac{2}{\sqrt{5}-1}\\\\=\dfrac{2(\sqrt{5}+1)}{(\sqrt{5}-1)(\sqrt{5}+1)}=\dfrac{2\sqrt{5}+2}{5-1}=\boxed{\dfrac{\sqrt{5}+1}{2}\approx1.618034}[/tex]
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Additional comment
You may notice that 1/x = x+1.
