Can You Solve for x in This Elegant Algebra Equation? | Olympiad Mathematics

Math olympiad problems like this one look impossible at first, but this math olympiad radical equation has a beautifully simple trick hidden inside. In this math olympiad challenge we solve the square root of x over one minus x, plus the square root of one minus x over x, equal to five over two. Watch step by step as we substitute variables, square both sides, spot the perfect cancellation that turns the messy middle term into a clean number, and reduce everything to a standard quadratic. Using the discriminant and the quadratic formula, we uncover both real solutions, x equals one fifth and x equals four fifths, then verify each answer in the original equation. If you love algebra, olympiad training, and satisfying math solutions, this walkthrough is made for you. Follow along, pause to try it yourself, and sharpen your problem solving skills. Subscribe to All About Math for a new challenge in every video. Drop a like if this helped and comment your favorite trick. #MathOlympiad #Algebra #MathChallenge