If y- y- y- = x+ x+ x+ , then dy d x =

Step-by-step solution

Given the equation: y- y- y- = x+ x+ x+ Let A = y- y- y- , which satisfies A = y - A . Squaring both sides yields A^2 = y - A , or equivalently A^2 + A - y = 0 . Similarly, let B = x+ x+ x+ , so B = x + B . Squaring gives B^2 = x + B , or B^2 - B - x = 0 . Since A = B by the given equality, denote their common value as K . Subtracting the two quadratic equations eliminates K^2 : (K^2 + K - y) - (K^2 - K - x) = 0 2K - y + x = 0 K = y - x 2 Substitute into K^2 - K - x = 0 : ( y - x 2 )^2 - ( y - x 2 ) - x = 0 Multipl