Question

X+1/x=radical 5
E(x)=(X^6+x^5-2x^4-3x^3-2x^2+x+1): x^3
=?

Answer 1

Răspuns:

Explicație pas cu pas:

E(x)= x³+x²-2x-3-2/x+1/x²+1/x³=x³+1/x³+x²+1/x²-2(x+1/x)-3

x+1/x=√5    (x+1/x)²=x²+1/x²+2=5    ⇒x²+1/x²=3

x+1/x)³=x³+3x²/x+3x/x²+1/x³=x³+3(x+1/x)+1/x³=5√5    x³+3√5+1/x³=5√5

 x³+1/x³=2√5

E(x)=2√5+3-2√5-3=0