Question

Знайти значення x,за якого числа x-1; 2x і 4x+6 утворюють геометричну прогресію ОООООООЧЕНЬ МНОГО БАЛОВ СРОЧНО ПОЖАЙЛУСТА

Answer 1

Надо использовать свойство прогрессии.

2x/(x-1)=(4x+6)/(2x).

Отсбда 4x² = (x-1)*(4x+6),

              4x² =  4x² + 2x - 6

После сокращения  4x² получаем:

0 =  2x - 6,

x = 6/2 = 3.

Ответ: х = 3.

             

Answer 2

Finding the Value of x for a Geometric Progression

To find the value of x for which the numbers x-1, 2x, and 4x+6 form a geometric progression, we can use the definition of a geometric progression and solve for x.

A geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Definition of Geometric Progression

A geometric progression is a sequence of numbers in which each term after the first is obtained by multiplying the preceding term by a fixed, non-zero number called the common ratio.

Solving for x

For the given sequence x-1, 2x, and 4x+6 to form a geometric progression, the following condition must be satisfied: 2x / (x-1) = (4x+6) / 2x

Let's solve for x using this condition.

Calculation

2x / (x-1) = (4x+6) / 2x Cross-multiply to get: (2x)^2 = (x-1)(4x+6) 4x^2 = 4x^2 + 6x - 4x - 6 0 = 6x - 6 6x = 6 x = 1

Conclusion

The value of x for which the numbers x-1, 2x, and 4x+6 form a geometric progression is x = 1.