Question

1)(x-2y)²+(x+2)²= 0;2)(x+3y-2)²+x²-10xy+25y= 0;3)(2x-y-3)+(x+3y-5)²= 0;​

Answer 1

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Пошаговое объяснение:

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Answer 2

It seems like you've provided three equations in the form of quadratic expressions set equal to zero. Let's analyze each of them separately:

1. $(x - 2y)^2 + (x + 2)^2 = 0$: In this equation, both terms are non-negative since they're squared. The only way for their sum to be equal to zero is if both terms individually are equal to zero:

• $x - 2y = 0$
• $x + 2 = 0$

However, there is no real solution that satisfies both equations simultaneously. This is because in the first equation, if $x - 2y = 0$, then $x$ must be equal to $2y$, which contradicts the second equation $x + 2 = 0$. Therefore, this system of equations has no real solutions.

2. $(x + 3y - 2)^2 + x^2 - 10xy + 25y = 0$: This equation is a bit more complex, but we can try to solve it step by step.

• Expand the squared term: $(x + 3y - 2)^2 = x^2 + 6xy + 9y^2 - 4x - 12y + 4$
• Substitute the expanded term into the equation: $x^2 + 6xy + 9y^2 - 4x - 12y + 4 + x^2 - 10xy + 25y = 0$
• Combine like terms: $2x^2 - 4x - 4xy + 9y^2 + 13y + 4 = 0$

This is a quadratic equation in terms of $x$ and $y$. Solving it directly might be challenging due to its complexity. You could try factoring it or using the quadratic formula to find potential solutions. Keep in mind that this equation might have complex solutions as well.

3. $(2x - y - 3) + (x + 3y - 5)^2 = 0$: First, expand the squared term: $(x + 3y - 5)^2 = x^2 + 6xy + 9y^2 - 10x - 30y + 25$ Then, substitute the expanded term into the equation: $2x - y - 3 + x^2 + 6xy + 9y^2 - 10x - 30y + 25 = 0$ Combine like terms: $x^2 + 6xy + 9y^2 - 8x - 31y + 22 = 0$

Similar to the second equation, this is a quadratic equation in terms of $x$ and $y$. You can apply the same methods to solve for potential solutions.

Remember that solving quadratic equations can sometimes lead to complex solutions, especially if the equations are not easily factorable. If you're looking for numerical solutions, you might consider using computational tools or software to find approximate solutions.