If x+ x=2, 0 < x < 2 then x 4

Step-by-step solution

Given x + x = 2 for 0 Substituting the given value yields ( x - x)(2) = 1 , so x - x = 1 2 . Adding this to the original equation gives 2 x = 5 2 , hence x = 5 4 and x = 4 5 . Using the half-angle identity, x = 2 ^2 x 2 - 1 leads to 2 ^2 x 2 = 9 5 , so x 2 = 3 10 since x 2 is in the first quadrant. Applying the half-angle formula again, ^2 x 4 = 1 - x 2 2 = 1 - 3 10 2 = 10 - 3 2 10 . Rationalizing the expression gives ^2 x 4 = 1 2(10 + 3 10 ) , and taking the positive square root (since x 4 is in the first quadrant