Question

1/x+2+1/x^2-2x=8/x^3-4x

Answer 1

Решение приложено. Ответ 3. Подставьте в уравнение, проверка это подтвердит.

Answer 2

1/(x+2)+1/[x(x-2)]=8/[x(x-2)(x+2)]
x(x-2)(x+2)≠0⇒x≠0;x≠2;x≠-2
1*(x²-2x)+1*(x+2)=8
x²-2x+x+2-8=0
x²-x-6=0
D=1+24=25>0
x1+x2=1 U x1*x2=-6
x1=3 U x2=-2 не удов усл
Ответ х=3

Answer 3

To solve the equation (1/x + 2) + (1/x^2 - 2x) = 8/(x^3 - 4x), we'll simplify the equation and find the common denominator.

Step 1: Find the common denominator: The common denominator for the fractions is x^3 - 4x.

Step 2: Multiply each term by the common denominator: (x^3 - 4x) * (1/x) + (x^3 - 4x) * 2 + (x^3 - 4x) * (1/x^2 - 2x) = (x^3 - 4x) * 8/(x^3 - 4x)

Simplifying the equation, we have: x^2 - 4 + (x^3 - 4x) * (1/x^2 - 2x) = 8

Step 3: Expand and simplify: x^2 - 4 + (x - 2) = 8

Combining like terms: x^2 + x - 6 = 8

Step 4: Rearrange the equation: x^2 + x - 14 = 0

Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula to find the solutions.

Step 5: Apply the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation x^2 + x - 14 = 0, the coefficients are: a = 1, b = 1, c = -14

Substituting the values into the quadratic formula, we get: x = (-1 ± √(1^2 - 4 * 1 * -14)) / (2 * 1)

Simplifying further: x = (-1 ± √(1 + 56)) / 2 x = (-1 ± √57) / 2

So the solutions to the equation (1/x + 2) + (1/x^2 - 2x) = 8/(x^3 - 4x) are: x = (-1 + √57) / 2 and x = (-1 - √57) / 2