If x and y are acute angles, such that x+ y= 3 2 and x+ y= 3 4 , then (x+y) equals

Step-by-step solution

Given x + y = 3 2 and x + y = 3 4 . Squaring both equations: ( x + y)^2 = ^2 x + ^2 y + 2 x y = 9 4 ( x + y)^2 = ^2 x + ^2 y + 2 x y = 9 16 Adding the two squared equations: ( ^2 x + ^2 x) + ( ^2 y + ^2 y) + 2( x y + x y) = 9 4 + 9 16 1 + 1 + 2 (x - y) = 36 + 9 16 = 45 16 2 (x - y) = 45 16 - 2 = 13 16 (x - y) = 13 32 Now, consider the product of the original equations: ( x + y)( x + y) = 3 2 3 4 = 9 8 x x + y y + x y + x y = 9 8 1 2 ( 2x + 2y) + (x + y) = 9 8 Using 2x + 2y = 2 (x + y) (x - y) : (x + y) (x - y) + (x