help with algebra

Hi Guest,

If they have an arithmetic mean of 18, this means: $\dfrac{x+y}{2}=18$

So, $x+y=36$

If they have a geometric mean of $\sqrt{47}$, this means: $\sqrt{xy}=\sqrt{47}$

Then, $xy=47$

Now, we want to find $x^2+y^2$

We can rewrite it as follows: $(x+y)^2-2xy$  [Check this by expanding it]

So: $x^2+y^2=(x+y)^2-2xy=(36)^2-2(47)=1296-94=1202$

I hope this helps.