How many real roots does the given equation have?

 ${(\mathrm{x}+1)}^2-{\mathrm{x}}^2=0$ 

Given :${(\mathrm{x}+1)}^2-{\mathrm{x}}^2=0$

Simplifying it further, we get:

x² + 2x + 1 - x² = 0

=> 2x + 1 = 0

=>  x = $-\frac{1}{2}$

Hence, there is only one real root.