\(4044*4044 = 16353936\)

Algebra Level 3

It is known the quadratic equation \[{ x }^{ 2 }\quad -\quad x\quad -\quad 1635798016357980\quad =\quad 0\] The quadratic equation can be rewritten as \((x\quad -\quad \alpha )(x\quad -\quad \beta )\quad =\quad 0\) whereas \(\alpha \quad >\quad \beta \). Calculate the result of \[\frac { \alpha \quad +\quad 4\left\lfloor { \alpha }^{ \frac { 1 }{ 2 } } \right\rfloor \quad -\quad { \alpha }^{ 0 } }{ \left\lfloor \frac { { \beta }^{ 2 } }{ 4000 } \right\rfloor \quad -\quad \left\lceil \frac { \beta }{ 800 } \right\rceil \quad +\quad { \left| { \beta }^{ 0 } \right| } } \]

Try not to use a calculator, however you may use the fact that is in the title of this question
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