Can You Solve This High School Algebra Quiz? Two Different Methods

Find x-1/x When ∛x-∛(x-14)=2 | Two Elegant Methods | Full Step by Step Solution In this math tutorial we solve a beautiful algebra problem — find x-1/x given that ∛x-∛(x-14) = 2. First, we substitute a = ∛x and b = ∛(x-14), then, find a³-b³, and ultimately show that ab = 1, which means x(x-14) = 1. From there we present two completely different methods for finding x-1/x. The first method is a one-line insight — simply divide both sides of x(x-14) = 1 by x and rearrange to read off x-1/x instantly. The second method solves the quadratic x(x-14) = 1 explicitly using completing the square, finds the values of x and 1/x, and computes x-1/x directly. Both methods are explained clearly and completely from start to finish. The contrast between the two methods is what makes this video genuinely valuable — the first shows the power of seeing the right algebraic shortcut, while the second builds complete understanding by finding the actual values of x. Together they give you both speed and depth. What you will learn: How to substitute a = ∛x and b = ∛(x-14) to simplify the cube root equation How to use the expansion of (a-b)^3 to show that ab = 1 How to conclude that x(x-14) = 1 from the substitution How to find x-1/x instantly by dividing x(x-14)=1 through by x How to solve x(x-14)=1 by completing the square and find all values of x How to compute x-1/x from the explicit values of x and verify both methods agree This type of elegant two-method solution appears in math olympiad training, IB Mathematics Higher Level, A-Level Mathematics, college entrance examinations, and advanced high school algebra courses. Knowing multiple solution paths for the same problem is one of the most powerful habits in competitive mathematics. If you found this helpful, give it a thumbs up, share it with a fellow math lover, and subscribe for weekly videos on algebra, calculus, number theory, and olympiad problem solving. Hit the notification bell so you never miss an upload Don’t forget to like 👍, subscribe    / @nonsomaths  , and hit the notification bell for more math tips and tricks! #maths #algebra #matholympiad #MathTutorial #highschoolmath