Group Them Carefully 5

Algebra Level 2

If we square the equation, x+1x=3x + \dfrac1x = \sqrt3 , we get

(x+1x)2=(3)2x2+1x2+2=3x2+1x2=1\begin{aligned} \left( x + \dfrac1x \right)^2 &=& (\sqrt3)^2 \\ x^2 + \dfrac1{x^2} + 2 &=& 3 \\ x^2 + \dfrac1{x^2} &=& 1 \end{aligned}

What is the value of the x8+1x8x^8 + \dfrac1{x^8} ?

Hint: Try squaring the equation again, what happens?

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