> Original Question: Let rands denote the two real roots of x^2−x√(5 + 1) = 0. Then determine r^8+s^8.
> Codex Input: Calculate the roots of $xˆ2 - x \sqrt{5} + 1 = 0. Call the two roots r and s. Calculate z = rˆ8 + sˆ8. Evaluatez as an integer. Use sympy.
> Codex Output: > from sympy import * > x = Symbol(’x’) > r = solve(x*2 - xsqrt(5) + 1, x)[0] > s = solve(x*2 - xsqrt(5) + 1, x)[1] > z = r*8 + s*8 > print(z.evalf())
> Solution: 47
If the solution did not have the derivation of the algebra, the solution is wrong in university math. Now solving these problems for application, this is quite interesting and powerful.
Demonstrating understanding of why we get to the solution IS mathematical reasoning (at this level). This paper demonstrates being able to leap across mathematical reasoning, but not the reasoning itself.