Question

При каких значениях переменной равны дроби 6/х и х/2х-6​

Answer 1

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Answer 2

To find the values of the variable x for which the fractions are equal, we need to set the two fractions equal to each other and solve for x.

The fractions are 6/x and x/(2x-6). So, we have the equation:

6/x = x/(2x-6)

To solve for x, we can cross-multiply:

6(2x-6) = x * x

12x - 36 = x^2

Now, let's bring all terms to one side of the equation:

x^2 - 12x + 36 = 0

Now, we have a quadratic equation. To solve for x, we can factor it or use the quadratic formula:

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -12, and c = 36 in our case.

Plugging in the values:

x = (12 ± √((-12)^2 - 4 * 1 * 36)) / 2 * 1

x = (12 ± √(144 - 144)) / 2

x = (12 ± √0) / 2

x = (12 ± 0) / 2

Now, we have two solutions:

1. x = (12 + 0) / 2 = 12 / 2 = 6
2. x = (12 - 0) / 2 = 12 / 2 = 6

So, the variable x is equal to 6 for the given fractions to be equal: 6/x = x/(2x-6) = 6/6 = 1.