(x^2+y^2)^2=(X^2-y^2)^2+(2xy)^2 determine the sum of the squares of two numbers if the difference of the squares of the numbers is 5 and te product of the number is 6
+500 \((x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2\)
The problem gives us that:
\(x^2-y^2 =5\)
and
\(xy =6\)
Realize that we already have all the necessary values to determine \(x^2+y^2 \) without individually solving for x or y
Substituting the values of \(x^2-y^2\) and \(xy\) that we already have:
\((x^2+y^2)^2 = (5)^2 + (2*6)^2\)
\((x^2+y^2)^2=25+(12)^2= 25 + 144 = 169\)
Now we square root both sides to get:
\(x^2+y^2 = \pm13\). The problem doesn't directly limit x and y to real numbers, so we could have an answer of -13(square rooting 169 gives a negative and positive solution). The implied answer however would be 13.
