Group Them Carefully 1

Algebra Level 2

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

(x+1x)2=32x2+1x2+2=9x2+1x2=7\begin{aligned} \left( x + \dfrac1x \right)^2 &=& 3^2 \\ x^2 + \dfrac1{x^2} + 2 &=& 9 \\ x^2 + \dfrac1{x^2} &=& 7 \end{aligned}

What is the value of the x4+1x4x^4 + \dfrac1{x^4} ?

Hint: Try squaring the equation again!

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