Question

210:(x+4)+9+210:(x-4)=27​

Answer 1

Ответ:

Вот ответ

Пошаговое объяснение:

вап

Answer 2

To solve the equation, we'll need to find the value of 'x' that satisfies the equation. Let's start by simplifying the equation step by step:

Step 1: Remove the parentheses by applying the distributive property: 210/(x+4) + 9 + 210/(x-4) = 27

Step 2: Get rid of fractions by multiplying every term by the least common multiple (LCM) of the denominators, which is (x+4)(x-4):

LCM = (x+4)(x-4)

Multiply all terms by LCM: LCM * (210/(x+4)) + LCM * 9 + LCM * (210/(x-4)) = LCM * 27

Step 3: Cancel out the denominators: 210(x-4) + 9(x+4)(x-4) + 210(x+4) = 27(x+4)(x-4)

Step 4: Expand and simplify: 210x - 840 + 9(x^2 - 4x + 4x - 16) + 210x + 840 = 27(x^2 - 4x + 4x - 16)

Combine like terms: 210x - 840 + 9(x^2 - 16) + 210x + 840 = 27(x^2 - 16)

Step 5: Expand further: 210x - 840 + 9x^2 - 144 + 210x + 840 = 27x^2 - 432

Step 6: Combine like terms: 9x^2 + 420x - 144 = 27x^2 - 432

Step 7: Move all terms to one side of the equation: 9x^2 + 420x - 27x^2 - 144 + 432 = 0

Step 8: Simplify: -18x^2 + 420x + 288 = 0

Step 9: Divide the entire equation by the common factor (6) to simplify: -3x^2 + 70x + 48 = 0

Step 10: Now, we can try to factor the quadratic equation, but it doesn't appear to have simple integer solutions. Instead, let's solve for 'x' using the quadratic formula:

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

In our case, a = -3, b = 70, and c = 48.

Step 11: Plug the values into the quadratic formula:

x = (-(70) ± √(70^2 - 4*(-3)48)) / 2(-3)

Step 12: Calculate the discriminant (the value inside the square root):

Discriminant = 70^2 - 4*(-3)*48 = 4900 + 576 = 5476

Step 13: Continue with the quadratic formula:

x = (-70 ± √5476) / (-6)

Step 14: Calculate the square root of the discriminant:

√5476 = 74

Step 15: Finally, find the two possible values for 'x':

x = (-70 + 74) / (-6) -> x = 4/(-6) -> x = -2/3

x = (-70 - 74) / (-6) -> x = -144/(-6) -> x = 24

So, the two solutions for the equation are x = -2/3 and x = 24.