(x+1/x)²=3²

asked by guest
on Mar 30, 2025 at 8:04 am



You asked:

Solve the equation (x+1x)2=32{\left( x + \frac{1}{x} \right)}^{2} = {3}^{2} for the variable xx.

MathBot Answer:

The 4 solutions to the equation are: x=−32−52≈−2.618034x=−32+52≈−0.38196601x=32−52≈0.38196601x=32+52≈2.618034\begin{aligned}x &= - \frac{3}{2} - \frac{\sqrt{5}}{2} \approx -2.618034\\x &= - \frac{3}{2} + \frac{\sqrt{5}}{2} \approx -0.38196601\\x &= \frac{3}{2} - \frac{\sqrt{5}}{2} \approx 0.38196601\\x &= \frac{3}{2} + \frac{\sqrt{5}}{2} \approx 2.618034\end{aligned}

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