Siam's inequality

Algebra Level 3

What is the minimum integer value of xx that satisfies the equation

xx+34=0?\lfloor{\sqrt{x}}\rfloor - \lfloor{\sqrt{x+34}}\rfloor=0 ?

This problem is posed by Siam H.

Details and assumptions

The function x:RZ\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z} refers to the greatest integer smaller than or equal to xx. For example 2.3=2\lfloor 2.3 \rfloor = 2 and 5=5\lfloor -5 \rfloor = -5.

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