Puzzles
Powerful quadratics
Find all real solutions to
$$(x^2-7x+11)^{(x^2-11x+30)}=1.$$
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If \(x^2-7x+11=1\) or \(x^2-11x+30=0\), then this is one. The solutions to these are \(x=2,5,\) and \(6\).
It could also be one if \(x^2-7x+11=-1\) and \(x^2-11x+30\) is even. This happens when \(x=3\) or \(4\).
Therefore all the solutions to this are \(x=2,3,4,5\) or \(6\).
