If you are going to solve the cubic by inspection to get a=7, you might as well just notice that x=11, y=3 is a solution by inspection (10^4 = 10000, 12^4 =144^2 ~ 20000, so x=11 is the obvious try), and then if you care about the complex roots you can just solve for the cubic in y and factor out y-3. Much more straightforward than all the substitutions with a and b.
If you are going to solve the cubic by inspection to get a=7, you might as well just notice that x=11, y=3 is a solution by inspection (10^4 = 10000, 12^4 =144^2 ~ 20000, so x=11 is the obvious try), and then if you care about the complex roots you can just solve for the cubic in y and factor out y-3. Much more straightforward than all the substitutions with a and b.
www.youtube.com/@aikendrum2908, Thank you! That's a cool way to solve this problem too. Thank you!
Man, improve your handwriting
Hi bro, I'll make an effort. Thanks!