Most People Get This WRONG: x + 1/x = 3, x² + 1/x² = ?

If x + 1/x = 3, what is x² + 1/x²? Most people square the 3 and say 9, but that's wrong. In this lesson Mia finds the answer without ever solving for x: square both sides, use (a + b)² = a² + 2ab + b², and watch the middle term turn into a plain 2. A picture of a square shows where that middle term comes from. Then she goes one level up and finds x³ + 1/x³ by multiplying the two results, and checks everything with the real value of x. ✏️ Try it first: pause at 0:30 and give it a go. 💬 Did you say 7 or 9? Tell us in the comments! Chapters 00:00 The problem 00:32 Two traps: saying 9, and solving for x 01:12 The shortcut: square both sides 01:35 Where the middle term comes from 01:58 x² + 1/x² = 7 02:40 Next level: x³ + 1/x³ 03:36 Checking with the real x 04:22 Your turn 🔔 Subscribe for more step-by-step math lessons. #math #maths #mathtricks #mathematics #puzzle #quiz #geometry #algebra #brainteaser #education