Question

Dacă x+1/x=3,sa se calculeze x la 4 + 1/x la 4

Answer 1

intai ridici la puterea a doua x + 1/x = 3, obtii x² + 1/x*x*2 + (1/x)² = 9 =>
x² + 2 + 1/x² = 9 => x² + 1/x² = 7. ridici la puterea a doua si suma asta:
(x² + 1/x²)² = x^4 + 1/x^2*x^2*2 + (1/x^2)^2 = x^4 + 2 + 1/x^4 = 49.
finalizezi: x^4 + 1/x^4 = 47

Answer 2

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$\boxed{(a+b)^{2}=a^{2}+2ab+b^{2}}$