find all complex solutions Find all complex solutions 3y2 4

find all complex solutions.

Solution

Let y² =x.Then the given equation changes to 3x+ 4 = x² or, x² - 3x - 4 = 0 or, x² -4x + x -4 = 0 or, x(x -4) +1(x -4) = 0 or, (x -4)(x + 1) = 0 so that either x = 4 or x = -1Thus either y² = 4 or, y² = -1. If y² =4, then y = ± 2 and if y² = -1, then y = ± i . Thus, the complex solutions are ± i.