Difference between revisions of "The Root of Root Conjecture"

(The Conjecture)
(The Conjecture)
 
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===The Conjecture===
 
===The Conjecture===
If it exists an expression that <math>\sqrt{a + 2 \sqrt{b}}</math> for <math>a \geq 0</math> and <math>b \geq 0</math>, then the solution must be such that, for some numbers <math>x</math> and <math>y</math>, <math>x+y=a</math> and <math>xy=b.</math>
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If it exists an expression that <math>\sqrt{a + 2 \sqrt{b}}</math> for <math>a \geq 0</math> and <math>b \geq 0</math>, then the solution can be simplified to <math>x + \sqrt{y},</math> for some numbers <math>x</math> and <math>y</math>, such that <math>x+y=a</math> and <math>xy=b.</math>

Latest revision as of 02:17, 23 December 2023

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Created on January 23, 2021 4:51 PM PT when mathboy282 discovered a pattern in a MSM post.

The Conjecture

If it exists an expression that $\sqrt{a + 2 \sqrt{b}}$ for $a \geq 0$ and $b \geq 0$, then the solution can be simplified to $x + \sqrt{y},$ for some numbers $x$ and $y$, such that $x+y=a$ and $xy=b.$