What is the number of <strong>REAL</strong> roots of the equation (x-1)^{2}+(x-3)^{2}+(x-5)^{2}=0?

Explanation

The sum of squares of real numbers is equal to zero if and only if each term is zero. This implies x-1=0, x-3=0, and x-5=0 simultaneously, which means x would have to be 1, 3, and 5 at the same time. Since no single real number can satisfy all these, there are no real roots.

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