Question

Решить уравнение x^2+2xy+y^2

Answer 1

уравнением это не назовешь, т.к нет знака =

это формула сокр. умножения

(х+y)^2

Answer 2

To solve the equation x^2 + 2xy + y^2 = 0, we can use a factoring technique. This equation represents a quadratic equation in two variables, x and y.

Step 1: Identify the common factors, if any. In this case, there are no common factors between x^2, 2xy, and y^2.

Step 2: Try factoring using the perfect square trinomial formula. The perfect square trinomial formula is (a + b)^2 = a^2 + 2ab + b^2. Comparing this with our equation, we can see that it matches the form of a perfect square trinomial:

x^2 + 2xy + y^2 = (x + y)^2.

Step 3: Set the equation equal to zero and solve for x and y. (x + y)^2 = 0.

To make the equation equal to zero, the only possibility is if (x + y) equals zero:

x + y = 0.

Now we have a linear equation in two variables, x and y. We can solve for one variable in terms of the other:

y = -x.

So, any solution that satisfies the original equation x^2 + 2xy + y^2 = 0 must also satisfy the linear equation y = -x.

In other words, the solutions to the original equation are all pairs of real numbers (x, y) that satisfy y = -x. This equation represents a straight line passing through the origin with a slope of -1. Therefore, the solutions are all points on this line.