If x , y, z are the sides of a right angled triangle, where z is the largest side, then 1 _ x+z y + 1 _ z-x y =

Step-by-step solution

Since x, y, z are the sides of a right-angled triangle and z is the largest side, z is the hypotenuse. By Pythagoras theorem, x^2 + y^2 = z^2 , which gives y^2 = z^2 - x^2 . The given expression is 1 _ x+z y + 1 _ z-x y . Using the property 1 _a b = _b a , the expression can be written as: _y (x+z) + _y (z-x) Using the property _a m + _a n = _a (mn) , we get: _y ((x+z)(z-x)) _y (z^2 - x^2) Substituting z^2 - x^2 = y^2 , we get: _y (y^2) = 2 _y y = 2 Answer: 2