Originally Posted by
HallsofIvy Assuming that it was really |x+y|= 25, then, by the "parallelogram rule" for vector addtion, x+ y is the one diagonal of a parallelogram having sides x and y and x- y is the other diagonal. You can find the angle in the triangle with sides x, y, and x+y by using the cosine law on a triangle with sides of length 25, 13, and 17, then use the cosine law on a triangle with sides x, y, and x- y, and the same angle, to find the length of x-y.
Or you could use the fact that $\displaystyle |x+y|= \sqrt{(x+y)\cdot(x-y)}$$\displaystyle = \sqrt{x\cdot x+ 2x\cdot y+ y\cdot y}= 25$ to argue that $\displaystyle x\cdot x+ 2 x\cdot y+ y\cdot y= 25^2= 625$. You can easily find $\displaystyle x\cdot x$ and $\displaystyle y\cdot y$ and then find $\displaystyle 2x\cdot y$. Now use the fact that $\displaystyle (x-y)\cdot(x-y)= x\cdot x- 2 x\cdot y+ y\cdot y$ to find |x-y|.