Let x and y be real numbers Show that if x notequalto y and

Let x and y be real numbers. Show that if x notequalto y and x, y greaterthanorequalto 0, then x^2 notequalto y^2

Solution

Let x and y be real numbers

If x² y² then x² - y² 0 and   (x-y) (x+y) 0

therefore (x-y) 0 or (x+y) 0 but  (x+y) 0 because x,y 0

x-y 0 is only true for x,y 0

therefore   x y

or

another method

if x=y then we need to prove x² = y² ,

proof : if x=y,

multiply both side by x, we have

xx = yx and therefore xx = y(y) (because x=y)

we get  x² = y² .