Semi Pythagoras Triplet?

Algebra Level 3

Let there be two real numbers \(a,b\) that satisfy the given equation:


The range of the values that \(a\) can take for some value of \(b\) that satisfies the equation above is of the form \([-x,x]\) for some \( x \geq 0 \).

What is the value of \(x\)?



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