If x y z are in ap and xyz+1) are in gp then
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2y=x+z
y=(x+z)/2
y^2= x(z+1)
or, (x+z)^2/4=xz+x
or, x^2+z^2+2xz=4xz+4x
or, x^2+z^2-2xz=4x
or, (x-z)^2=4x
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