Question

при каком значении x числа 3x-2, x+2 и x+8 будут последовательными членами геометрической прогрессии?​

Answer 1

Ответ:

при х=1 и х=-10

Пошаговое объяснение:

$(b_n)\; \; 3x-2;x+2;x+8;...\\x=?\\\\b_1=3x-2\\b_2=x+2\\b_3=x+8\\\\q=\frac{b_2}{b_1}=\frac{b_3}{b_2}\\\\\frac{x+2}{3x-2}=\frac{x+8}{x+2}\\\\(3x-2)(x+8)=(x+2)^2\\\\3x^2-2x+24x-16=x^2+4x+4\\\\2x^2+18x-20=0\; \; |:2\\\\x^2+9x-10=0\\\\\left \{ {{x_1*x_2=-10} \atop {x_1+x_2=-9}} \right.= > x_1=-10;x_2=1$

Answer 2

Identifying Geometric Progression

To determine when the values of x, 3x-2, x+2, and x+8 will form a geometric progression, we can use the definition of a geometric progression. In a geometric progression, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Calculating the Common Ratio

The common ratio (r) for a geometric progression can be found by dividing any term in the sequence by its preceding term. In this case, we can calculate the common ratio for the given terms as follows:

1. The common ratio between the second and first terms (3x-2 and x) is: (3x-2) / x 2. The common ratio between the third and second terms (x+2 and 3x-2) is: (x+2) / (3x-2) 3. The common ratio between the fourth and third terms (x+8 and x+2) is: (x+8) / (x+2)

Conclusion

For the values of x, 3x-2, x+2, and x+8 to form a geometric progression, the common ratio between consecutive terms should be the same. Therefore, we need to solve the equations for the common ratios and find the value of x that satisfies this condition.