Question

Найдите все значения a, при которых корень уравнения (a-1)x=6 является натуральным числом.

Answer 1

Чтобы корень уравнения был натуральным числом, коэффициент при х (а-1) должен быть делителем шести. это выполняется при а=2; 3; 4; 7.

Answer 2

(а-1)х=6
х=6/(а-1)
Чтобы корень был натуральным, нужно чтобы (а-1) было делителем 6 и а≠1
а=2;3;4;7

Answer 3

Finding the Values of 'a' for which the Root of the Equation is a Natural Number

To find the values of 'a' for which the root of the equation `(a-1)x=6` is a natural number, we need to solve the equation and determine the values of 'a' that satisfy the condition.

Let's solve the equation step by step:

1. Start with the equation `(a-1)x=6`. 2. Divide both sides of the equation by `(a-1)` to isolate 'x': `x = 6/(a-1)`.

Now, we need to find the values of 'a' for which 'x' is a natural number.

A natural number is a positive integer (1, 2, 3, 4, ...).

To find the values of 'a', we can substitute different natural numbers for 'x' and solve for 'a'.

Let's substitute some natural numbers for 'x' and solve for 'a':

1. If 'x' is 1, then `1 = 6/(a-1)`. Solving for 'a', we get `a = 7`. 2. If 'x' is 2, then `2 = 6/(a-1)`. Solving for 'a', we get `a = 4`. 3. If 'x' is 3, then `3 = 6/(a-1)`. Solving for 'a', we get `a = 3`. 4. If 'x' is 4, then `4 = 6/(a-1)`. Solving for 'a', we get `a = 2`. 5. If 'x' is 5, then `5 = 6/(a-1)`. Solving for 'a', we get `a = 7/5`.

Therefore, the values of 'a' for which the root of the equation `(a-1)x=6` is a natural number are: a = 7, 4, 3, 2, and 7/5.

Please note that these values are obtained by substituting natural numbers for 'x' and solving for 'a'. There may be other values of 'a' that satisfy the condition, but these are the ones we found based on the given equation.

I hope this helps! Let me know if you have any further questions.