To solve the equation x^(3)-3x^(2)-4=(1)/(x-1)+5, we need to get rid of the fraction first.
Multiplying every term by (x-1) yields:
(x-1)(x^(3)-3x^(2)-4)= [1/(x-1)](x-1) + [5(x-1)]
Expanding and simplifying both sides:
x^(4)-3x^(3)-4x-5(x-1) = 1 + 5x - 5
x^(4)-3x^(3)-4x-5x + 5 = 1 + 5x - 5
x^(4)-3x^(3)-9x + 1 = 5x - 5
Moving all terms to the left side of the equation:
x^(4)-3x^(3)-9x - 5x + 1 - 5 = 0
x^(4)-3x^(3)-14x - 4 = 0
Now, we need to find the roots of this fourth degree polynomial equation. Unfortunately, there is no simple algebraic method to find the exact roots for polynomials of degree 4 or higher. However, we can use numerical methods or calculators to approximate the roots.
x^(3)-3x^(2)-4=(1)/(x-1)+5
solve for x
1 answer
1 answer