Answer:
The provement is below
Step-by-step explanation:
z^(1/2)=x^(1/2)+y^(1/2) => (z^(1/2))^2= (x^(1/2)+y^(1/2))^2
=> z=x+y+2*x^(1/2)*y^(1/2) => z-x-y= 2*x^(1/2)*y^(1/2)
=> (z-x-y)^2= (2*x^(1/2)*y^(1/2) )^2 => (z-x-y)^2=4*x*y (1)
Pls note that (z-x-y)^2= ((-1)*(-1)*(z-x-y))^2= ((-1)*(x+y-z))^2= (-1)^2*(x+y-z)^2=
=(x+y-z)^2
So (z-x-y)^2= (x+y-z)^2 !!! Substitute in (1) (z-x-y)^2 by (x+y-z)^2 and will get
the required equality (x+y-z)^2=4*x*y
