The number of common solutions of the pair of equations 2 ^2 - 2 ^2 + 1 = 0 and 2 ^2 + 3 - 2 = 0 in the interval [0, 2 ] , is

Step-by-step solution

Given the second equation: 2 ^2 + 3 - 2 = 0 (2 - 1)( + 2) = 0 Since [-1, 1] , = -2 is rejected. Thus, = 1 2 . Given the first equation: 2 ^2 - 2 ^2 + 1 = 0 2 ^2 - 2(1 - ^2 ) + 1 = 0 4 ^2 - 1 = 0 ^2 = 1 4 = 1 2 The common solution for both equations is = 1 2 . In the interval [0, 2 ] , the solutions for = 1 2 are = 6 and = 5 6 . Therefore, the number of common solutions is 2 . Answer: 2