Question

Help me answer this question for 5.b)

Answer 1

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