<s>[INST] How to solve $(x-2)^4+(x-3)^4=1$? I'm trying my hand on these types of expressions. how to solve $x$ and $y$ in $\displaystyle(x-2)^4+(x-3)^4=1$    and   $\displaystyle (y-1)(y-2)(y-3)(y-4)=1$?
   please write step by step solution !  thank u
 [/INST] HINTS
case 1: $2$ and $3$ are obvious solutions. Divide the polynom by $(x-2)(x-3)$ and solve the result.
case 2: $(y-1)(y-2)(y-3)(y-4) = [(y^2−5y)+5]^2−1$ see this post about (y-1)(y-2)(y-3)(y-4)
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