A graph (a,b) shows the two equations appear to have one point in common: (1+sqrt3 ,1-sqrt3) from which a^4+b^4 = 56
https://www.desmos.com/calculator/l0nucubtco
If you add the equations together you can rearrange the result as
a^4-4a^3+8a+4 = -(b^4-4b^4+8b+4)
whose graph is just four dots: (1+/+/-/-sqrt3 , 1+/-/+/-sqrt3)
Subtracting the two equations gives a sextic curve that goes through the right one.
Guessing the equality (from adding) works when both sides are zero we can graph the quartic a^4-4a^3+8a+4 which has two double roots at 1+/=sqrt3.
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Posted by Jer
on 2024-09-15 19:52:59 |
solution by graphing