Question

В системе счисления с некоторым основанием 144 в десятичной сс записывается 264 в x сс. Найти основания​

Answer 1

Ответ:

2*x^2+6*x+4=144

x=7 (подходит только положительный корень)

Объяснение:

Answer 2

Converting from Decimal to Base-x

To find the base of the number system, we need to convert the given decimal number (264) to the base-x number system. The base of the number system will be the same as the base-x.

Let's go step by step to find the base of the number system:

1. Convert the decimal number (264) to the base-x number system. 2. Set up an equation using the given information: 144 in the base-x number system is equal to 264 in the decimal number system.

Conversion Calculation

To convert a decimal number to a base-x number, we can use the following formula:

264 = a * x^2 + b * x^1 + c * x^0

Where: - a, b, and c are the digits in the base-x number system. - x is the base of the number system.

Let's solve this equation to find the values of a, b, c, and x.

Solving the Equation

We know that 264 is equal to 1 * x^2 + 4 * x^1 + 4 * x^0 in the base-x number system.

From the equation, we can deduce that the base of the number system (x) must be greater than or equal to 5, as the digits in the base-x number system can only range from 0 to x-1.

Now, let's substitute the values of a, b, and c with their respective digits in the base-x number system:

264 = 1 * x^2 + 4 * x^1 + 4 * x^0

Simplifying the equation, we get:

264 = x^2 + 4x + 4

Now, we need to solve this quadratic equation to find the possible values of x.

Solving the Quadratic Equation

To solve the quadratic equation, we can set it equal to zero:

x^2 + 4x + 4 - 264 = 0

Simplifying further, we get:

x^2 + 4x - 260 = 0

Using the quadratic formula, we can find the values of x:

x = (-b ± √(b^2 - 4ac)) / 2a

For our equation, a = 1, b = 4, and c = -260.

Solving the quadratic equation, we find two possible values for x: x = 10 and x = -26.

However, since the base of a number system cannot be negative, we can discard the value x = -26.

Therefore, the base of the number system is x = 10.

Conclusion

In the given number system, where 144 in the base-x number system is equal to 264 in the decimal number system, the base of the number system is 10.

Please let me know if you need any further assistance!