Question

Consider the following statement There are real numbers and such that Va+ V + b in the box below, as an ordered, comma that satisfy the property. Show that you can do this by entering appropriate values for a and To prove the statement, it suffices to find values of a and separated list of two numbers (,) -

Answer 1

Answer:

a=0, b=16, of the pair (0,16)

Step-by-step explanation:

You want to prove the following: There are real numbers a and b such that $\sqrt{a+b}=\sqrt{a}+\sqrt{b}$

So, to prove this, it is enough to find a pair (a,b) of real numbers for which the equation holds true. There are infinite of such pairs, but one example is (0,16). Indeed:

$\sqrt{a+b}=\sqrt{0+16}=\sqrt{16}=4=0+4=\sqrt{0}+\sqrt{16}=\sqrt{a}+\sqrt{b}$

In fact, (0,m) or (n,0) ara valid pairs, for nonnegative numbers m,n. Even more is true; these are the only pairs which satisfy the equation.