Question 256524
<font face="Garamond" size="+2">


Let *[tex \Large x] represent the short leg, then *[tex \Large x\,+\,7] represents the long leg, and we are given that the hypotenuse is 17.  Pythagoras says (or would have said if he were still alive, that is):


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ \left(x\,+\,7\right)^2\ =\ 17^2]


Expand, collect terms, and put the quadratic into standard form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ x^2\ +\ 14x\ +\ 49\ -\ 289\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x^2\ +\ 14x\ -\ 240\ =\ 0]


Factor out the unnecessary 2:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 7x\ -\ 120\ =\ 0]


The quadratic factors.  {Hint: -8 times 15 = -120 and -8 plus 15 = 7}.  Exclude the negative root.  Your answer is the positive root.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
</font>