Find the numbers of non-zero integral solutions of the equation `|1-i|^(x) =2^(x)`

Find the number of non-negative integral solutions of the equation x+y+z=10.

Find the number of positive integral solutions of the equation x+y+z=12.

Find the number of real solutions to the equation log_(0.5)x=|x| .

Find the number of positive integral solution of the equation tan^(-1)x+cos^(-1)(y/(sqrt(1+y^2)))=sin^(-1)(3/(sqrt(10)))

Find the number of positive integral solution of the equation tan^(-1)x+cos^(-1)y/(sqrt(1-y^2))=sin^(-1)3/(sqrt(10))

Let f (x)= x^3 -3x+1. Find the number of different real solution of the equation f (f(x) =0

Find the number of non-negative integer solutions of equation x+y+z+2w=20.

Find the number of positive integral solutions of x y z=21600.

Find the number of positive integral solutions satisfying the equation (x_1+x_2+x_3)(y_1+y_2)=77.

Find the number of non-negative integral solutions of x+y+z+wlt=20.