Question

3Х-3У+Х^2-ХУ^2=36Х^3-Х=

Answer 1

х(36x^2 -1) = x(6x-1)(6x+1)

Answer 2

To solve the equation 3X - 3Y + X^2 - XY^2 = 36X^3 - X = 0, we'll break it down into steps:

1. Combine like terms: X^3 + X^2 - XY^2 + 3X - 3Y - X = 0

2. Rearrange the terms: X^3 + X^2 - XY^2 + 2X - 3Y = 0

3. Factor out common terms: X(X^2 + X - Y^2 + 2) - 3Y = 0

4. Set each factor equal to zero: X = 0 (Equation 1) X^2 + X - Y^2 + 2 = 0 (Equation 2) -3Y = 0 (Equation 3)

Now let's solve each equation individually:

Equation 3: -3Y = 0 This equation implies that Y = 0.

Equation 1: X = 0 From this equation, we find that X = 0.

Equation 2: X^2 + X - Y^2 + 2 = 0 Since we already found X = 0 and Y = 0, we substitute these values into Equation 2: (0)^2 + 0 - (0)^2 + 2 = 0 0 + 0 + 0 + 2 = 0 2 ≠ 0

Therefore, there are no real solutions for X and Y that satisfy the original equation.