Question

repede ca i au 2 ,ex 3 va rog repede​

Answer 1

Răspuns:

$b_5=b_1\cdot q^4$

$b_4=b_1\cdot q^3$

$b_2=b_1\cdot q$

Inlocuind in sistem, obtinem:

$b_5-b_1=b_1\cdot q^4 - b_1 = b_1(q^4-1)=30$

$b_4-b_2=b_1\cdot q^3 - b_1\cdot q=b_1 q(q^2-1)=12$

Impartind cele doua ecuatii, se obtine:

$\frac{b_1(q^4-1)}{b_1 q(q^2-1)} = \frac{(q^2-1)(q^2+1)}{q(q^2-1)}=\frac{q^2+1}{q}=\frac{30}{12}=\frac{5}{2}$

Deci $2(q^2+1)=5q$, de unde $2q^2-5q+2=0$.

$\Delta=25-16=9$, $q_{1,2}=\frac{5\pm 3}{4}$.

$q_1=\frac{1}{2},\; q_2=2$.

Daca $q=\frac{1}{2}$ atunci $b_1 \cdot (\frac{1}{16}-1)=30$

adica $-b_1\cdot \frac{15}{16}=30$ deci $b_1=-32$

Daca $q=2$ atunci $b_1\cdot 15 =30$ deci $b_1=2$.

Explicație pas cu pas: