x+1/x =4
x²
asked by guest on Mar 29, 2025 at 3:16 am
MathBot Answer:
x2∈{(3+2)2,(2−3)2}x^{2} \in \left\{\left(\sqrt{3} + 2\right)^{2}, \left(2 - \sqrt{3}\right)^{2}\right\}x2∈{(3+2)2,(2−3)2}
The 2 solutions to the equation are: x=2+3≈3.7320508x=2−3≈0.26794919\begin{aligned}x &= 2 + \sqrt{3} \approx 3.7320508\\x &= 2 - \sqrt{3} \approx 0.26794919\end{aligned}xx=2+3≈3.7320508=2−3≈0.26794919
By substituting this value into the expression, we find that: x2=(3+2)2=(3+2)2\begin{aligned}x^{2} &= \left(\sqrt{3} + 2\right)^{2}\\&= \left(\sqrt{3} + 2\right)^{2}\end{aligned}x2=(3+2)2=(3+2)2
