The number of real roots of the equation $$(x − 1)^{2} + (x − 3)^{2} + (x − 5)^{2} = 0$$​ is:

Correct option is A

Given:
​$$(x − 1)^{2} + (x − 3)^{2} + (x − 5)^{2} = 0$$​​
Formula used:​
A sum of squares of real numbers is zero if and only if each square term is zero.​
Solution:
​$$(x − 1)^{2} ≥ 0\\(x − 3)^{2} ≥ 0\\(x − 5)^{2} ≥ 0$$​​
For the sum to be zero:
​$$x − 1 = 0\\x − 3 = 0\\x − 5 = 0$$​​
These equations cannot be satisfied simultaneously.
Hence, the given equation has no real solution.
The correct answer is (a) 0.