Răspuns:
Explicație pas cu pas:
x - 1/x = 3
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a)
(x - 1/x)² = 3²
-> aplic formula ( a - b)² = a² - 2ab + b²; unde a = x, iar b = 1/x
x² - 2 × x × 1/x + 1/x² = 9
2× (x/x) = 2 × 1 = 2
x² - 2 + 1/x² = 9
x² + 1/x² = 9 + 2
x² + 1/x² = 11
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b)
( x - 1/x)³ = 3³
x³ - 1/x³ - 3 ×x×1/x ( x - 1/x) = 27
x³ - 1/x³ - 3 × 3 = 27
x³ - 1/x³ = 27 + 9
x³ - 1/x³ = 36
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c)
( x - 1/x)² = 3²
x² + 1/x² = 11 -> ridic relatia din nou la patrat
(x² + 1/x²)² = 11²
x⁴ + 1/x⁴+ 2x²/x² = 121
2x²/x² = 2
x⁴ + 1/x⁴ = 121 - 2
x⁴ + 1/x⁴ = 119
