To solve this equation, we will first expand both sides of the equation and simplify:
For the left side of the equation(х-1)(х-4)(х+7) = (х^2 - 4х - х + 4)(х+7) = (х^2 - 5х + 4)(х+7) = х^3 + 7х^2 - 5х^2 - 35x + 4x + 28 = х^3 + 2х^2 - 31x + 28
For the right side of the equationх(х+1)^2 = х(х^2 + 2x + 1) = х^3 + 2x^2 + x
Now we set the two sides of the equation equal to each other and simplify:
х^3 + 2х^2 - 31x + 28 = х^3 + 2x^2 + Rearranging terms2х^2 - 31x + 28 = 2x^2 + x
Solving for x, we get-31x + 28 = Combining like terms-31x - x = -2-32x = -2x = -28 / -3x = 7/8
Therefore, the solution to the equation is x = 7/8.
To solve this equation, we will first expand both sides of the equation and simplify:
For the left side of the equation
(х-1)(х-4)(х+7) = (х^2 - 4х - х + 4)(х+7) = (х^2 - 5х + 4)(х+7) = х^3 + 7х^2 - 5х^2 - 35x + 4x + 28 = х^3 + 2х^2 - 31x + 28
For the right side of the equation
х(х+1)^2 = х(х^2 + 2x + 1) = х^3 + 2x^2 + x
Now we set the two sides of the equation equal to each other and simplify:
х^3 + 2х^2 - 31x + 28 = х^3 + 2x^2 +
Rearranging terms
2х^2 - 31x + 28 = 2x^2 + x
Solving for x, we get
-31x + 28 =
Combining like terms
-31x - x = -2
-32x = -2
x = -28 / -3
x = 7/8
Therefore, the solution to the equation is x = 7/8.