Problem
ALG-B1-M03-P007 Returning from Two Substitutions
#7
★★☆☆☆ Level 2 of 5
Solve \(x^4-13x^2+36=0\).
Set \(u=x^2\), then solve the quadratic equation in \(u\).
We get \(u^2-13u+36=0\), so \((u-4)(u-9)=0\).
Since \(u=x^2\), we have \(x^2=4\) or \(x^2=9\). Hence \(x=\pm2,\pm3\).
Standard practice in moving to and from a substitution.