Odpowiedzi

2010-02-27T20:26:28+01:00
Dane jest wyrażenie W(x) = x³-2x²-3x
x⁶-18x⁴+81x²


a) x∈R/{-3,0,3}
b)
x³-2x²-3x
W(x) =--------------- =
x⁶-18x⁴+81x²
(x+1)(x-3)
=----------------=
x(x²-9)²
x+1
=----------------
x(x²-9)(x+3)
  • Użytkownik Zadane
2010-02-27T22:32:41+01:00
W(x)=(x³-2x²-3x)/(x^6-18x^4+81x²)

a)
D: x^6-18x^4+81x²≠0
x²(x^4-18x²+81)≠0 /:x²
(x²-9)²≠0
(x-3)(x+3)≠0
x1≠-3 I x2≠3
D=R\{-3;3}

b)
W(x)=(x³-2x²-3x)/(x^6-18x^4+81x²)=[x(x²-2x-3)]/[x²(x^4-18x²+81)]=[(x+1)(x-3)]/[x²(x-3)(x+3)]=(x-1)/[x(x+3)]