Caerswso1pc

2022-03-31

Solving for x in a (modified) quadratic

${\left(\sqrt{49+20\sqrt{6}}\right)}^{\sqrt{a\sqrt{a\sqrt{a\cdots \mathrm{\infty}}}}}+{(5-2\sqrt{6})}^{{x}^{2}+x-3-\sqrt{x\sqrt{x\sqrt{x}\cdots \mathrm{\infty}}}}=10$

where$\text{}\text{where}\text{}a={x}^{2}-3,(a\ne 0),\text{}\text{Solve for}\text{}\text{}x$

where

Harry Gibson

Beginner2022-04-01Added 13 answers

There is nothing wrong but if $x=\pm \sqrt{2}$ then $a=-1<0$ so $\sqrt{a\sqrt{a\cdots}}$ is not well-defined. Hence, $x=\pm \sqrt{2}$ must be "disqualified" as a solution.

Usually it is always good to check all solutions you got with the original equation since we usually only prove the direction that if x satisfies then equation then x is equal to this and this, but we actually want to prove the other direction as well.

Usually it is always good to check all solutions you got with the original equation since we usually only prove the direction that if x satisfies then equation then x is equal to this and this, but we actually want to prove the other direction as well.

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