Вправи 401 - 467 » 412

412. Обчисліть x2 + x–2, якщо: 1) якщо x + x–1 = 3, то x2 + x–2 = x2 + (x–1)2 + 2x • x–1 – 2x • x–1 = (x + x–1)2 – 2x • x–1 = 32 – 2 • 1 = 9 – 2 = 7. 2) якщо x – 1/x = 9, то x2 + x–2 = x2 + (x–1)2 – 2x • x–1 + 2x • x–1 = (x + x–1)2 + 2x • x–1 = (x – 1/x)2 + 2 • 1 = 92 + 2 = 81 + 2 = 83.