Question

vă rog la 24 ..................

Answer 1

E (x)=x^5 -5x^3 +4x=

x(x^4 -5x^2+4)=

x(x^4-x^2-4x^2+4)=

x[x^2 (x^2 -1)-4(x^2 -1)]=

x(x^2 -1)(x^2 -4)=

=x(x-1)(x+1)(x-2)(x+2)

E (a)= (a-2)(a-1)a (a+1)(a+2) => produsul a cinci numere intregi consecutive

=> ca sunt doua numere pare dintre care unul divizibil cu 2, iar celalalt divizibil cu 4

=>exista un numar divizibil cu 3

=>exista un numar divizibil cu 5

2×3×4×5=120 => E (a) divizibil 120

b)

(x+3)(x-2)(x-1)x (x+1)(x+2) / [(x-1)(x-2)]

=[(x+3)x] • [(x+1)(x+2)]

=(x^2 +3x)(x^2 +3x+2) adevărat

c)

(x-2)(x-1)x (x+1)(x+2)/[x (x^2+2x+1)]=x (x-1)

(x-2)(x-1)(x+1)(x+2)/(x^2 +2x+1)=x (x-1)

(x-2)(x+1)(x+2)=x (x^2 +2x+1)

(x^2 -x-2)(x+2)=x^3 +2x^2 +x

x^3+2x^2-x^2-2x-2x-4=x^3+2x^2+x

X^2 +5x+4=0

X^2+x+4x+4=0

(X+1)(x+4)=0

x+1=0=>x= -1

x+4=0=>x= -4

d)

F (x)=x (x^2-3x+2)/E (x)

=x (x-2)(x-1)/[(x-2)(x-1)x (x+1)(x+2)]

=1/[(x+1)(x+2)]

S=1/(1•2) +1/(2•3) +..+1/(101•102)

=1/1 -1/2 +1/2 -1/3+...+1/100 -1/101+1/101 -1/102

=1/1 -1/102

=(102-1)/102

S=101/102