Question

X-23/3x-23=x-23/2.3x-2

Answer 1

Ответ: на фото

Объяснение:

Answer 2

To solve the equation (X-23)/(3X-23) = (X-23)/(2.3X-2), we can start by multiplying both sides of the equation by (3X-23)(2.3X-2) to eliminate the denominators. This gives us:

(2.3X-2)(X-23) = (3X-23)(X-23)

Expanding both sides of the equation:

(2.3X^2 - 52.9X - 2X + 46) = (3X^2 - 69X - 23X + 529)

Combining like terms:

2.3X^2 - 54.9X + 46 = 3X^2 - 92X + 529

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

2.3X^2 - 54.9X + 46 - 3X^2 + 92X - 529 = 0

Combining like terms again:

-0.7X^2 + 37.1X - 483 = 0

Now, we have a quadratic equation. To solve it, we can either factor, complete the square, or use the quadratic formula. However, upon examination, this quadratic equation does not factor nicely, so we'll resort to using the quadratic formula:

X = (-b ± √(b^2 - 4ac))/(2a)

For our equation -0.7X^2 + 37.1X - 483 = 0, the coefficients are a = -0.7, b = 37.1, and c = -483. Substituting these values into the quadratic formula:

X = (-37.1 ± √(37.1^2 - 4(-0.7)(-483)))/(2(-0.7))

Simplifying further:

X = (-37.1 ± √(1376.41 - 1354.8))/(2(-0.7)) X = (-37.1 ± √21.61)/(-1.4)

Finally, we can evaluate the two possible solutions:

X = (-37.1 + √21.61)/(-1.4) ≈ 31.364 X = (-37.1 - √21.61)/(-1.4) ≈ 0.736

So the two solutions to the equation are approximately X ≈ 31.364 and X ≈ 0.736.