For a real number x ≠ 0, it is known that (x − 1/x)² =

Intro: ‍1. It is known that a + b = −7, ab =

Find: a) (a + b)² b) a² + b² c) (a − b)² d) a² − ab + b² e) a³ + b³

Find all values of: a) x − 1/x b) x + 1/x c) (x + 1/x)² d) x³ − 1/x³ Inequalitie

Prove that for all values of x the following inequalities hold: a) x² + 2x + 1 ≥

Prove for all a and b the inequalities: a) a² + b² ≥ 2ab b) (c²a²)/2 + (b²)/(2c²

a) What is the minimum value of 32x² + 1/(8x²) for x ≠ 0? b) At which x is the m

Find all pairs of natural numbers x and y satisfying the equation: a) x² − y² =

Prove that two natural number squares cannot differ by 14.

For any a, b, c > 0 prove the inequalities: a) a² + b² + c² ≥ ab + bc + ac b) (a

a) Derive the formula (a + b + c)². b) It is known that a + b + c = 5 and ab + b

What can a² + b² + c² be? c) It is known that x + y + z =

Get more from Problems