Problem 9

Let's take a look at [tex]\((x + y)^2\)[/tex] and [tex]\(2 + y^2\)[/tex]. While Beeker believes that these two expressions are equal for all real numbers [tex]\(x\)[/tex] and [tex]\(y\)[/tex], Clod believes they are not. Let's get to the bottom of this!

a) Evaluate [tex]\((x + y)^2\)[/tex] and [tex]\(2 + y^2\)[/tex] for [tex]\(x = 7\)[/tex] and [tex]\(y = 11\)[/tex].

b) For which values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] does [tex]\((x + y)^2\)[/tex] equal [tex]\(2 + y^2\)[/tex]? For which values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] does [tex]\((x + y)^2\)[/tex] not equal [tex]\(2 + y^2\)[/tex]?

Hint: Get Hint