Let x, y (0, 2 ) be such that (x+y) = 2 (x-y) and 5 (x+y) = 3 (x-y) . Then the value of ^2 x is equal to

Step-by-step solution

Given (x+y) = 2 (x-y) (x+y) (x-y) = 2 1 Applying componendo and dividendo: (x+y)+ (x-y) (x+y)- (x-y) = 2+1 2-1 2 x y 2 x y = 3 x y = 3 (1) Also given 5 (x+y) = 3 (x-y) (x+y) (x-y) = 3 5 Applying componendo and dividendo: (x+y)+ (x-y) (x+y)- (x-y) = 3+5 3-5 2 x y -2 x y = 8 -2 - x y = -4 x y = 1 4 (2) Multiplying equations (1) and (2): ( x y ) ( x y) = 3 1 4 ^2 x = 3 4 Answer: 3 4