Question

X(1-X)+x (x^2-1)=x^2 (x-1)

Answer 1

X-x^2+x^3-x=x^3-x^2
2x

Answer 2

To solve the equation $X(1-X)+x (x^2-1)=x^2 (x-1)$, we can follow these steps:

Step 1: Distribute the terms on both sides of the equation: $X - X^2 + x^3 - x = x^3 - x^2$

Step 2: Group the like terms on one side of the equation: $X - X^2 + x^3 - x^3 + x^2 - x = 0$

Step 3: Simplify the equation: $X - X^2 = 0$

Step 4: Factor out an $X$ from the left-hand side: $X(1 - X) = 0$

Now, we have two possible solutions:

1. $X = 0$
2. $1 - X = 0 \Rightarrow X = 1$

So, the solutions for the equation are $X = 0$ and $X = 1$.