If p-1 upon p = 3 then find the value of p^2+1 upon p^2
You asked:
MathBot Answer:
\(p^{2} + \frac{1}{p^{2}} \in \left\{\left(\frac{3}{2} - \frac{\sqrt{13}}{2}\right)^{2} + \frac{1}{\left(\frac{3}{2} - \frac{\sqrt{13}}{2}\right)^{2}}, \frac{1}{\left(\frac{3}{2} + \frac{\sqrt{13}}{2}\right)^{2}} + \left(\frac{3}{2} + \frac{\sqrt{13}}{2}\right)^{2}\right\}\)
The 2 solutions to the equation are: \[\begin{aligned}p &= \frac{3}{2} - \frac{\sqrt{13}}{2} \approx -0.30277564\\p &= \frac{3}{2} + \frac{\sqrt{13}}{2} \approx 3.3027756\end{aligned}\]
By substituting this value into the expression, we find that: $$\begin{aligned}p^{2} + \frac{1}{p^{2}} &= \left(\frac{3}{2} - \frac{\sqrt{13}}{2}\right)^{2} + \frac{1}{\left(\frac{3}{2} - \frac{\sqrt{13}}{2}\right)^{2}}\\&= \left(\frac{3}{2} - \frac{\sqrt{13}}{2}\right)^{2} + \frac{1}{\left(\frac{3}{2} - \frac{\sqrt{13}}{2}\right)^{2}}\end{aligned}$$