Question

X² + y² < 4x² - y²>0​

Answer 1

смотри прикреплённое изображение ===>>

Answer 2

Ответ:

Объяснение:

Ответ приложен

Answer 3

The expression you provided is a system of inequalities involving quadratic terms. Let's break it down and analyze each inequality separately.

1. x² + y² < 4x²: This inequality represents a region in the xy-plane where the sum of the squares of x and y is less than four times the square of x. To simplify this inequality, let's move all the terms to one side: 0 < 3x² - y²

2. 4x² - y² > 0: This inequality represents a region in the xy-plane where four times the square of x is greater than the square of y. To simplify this inequality, let's move all the terms to one side: 0 < y² - 4x²

Now, we have the following system of inequalities: 0 < 3x² - y² 0 < y² - 4x²

To better understand the solution, we can consider the graphs of these inequalities.

In the first inequality, 0 < 3x² - y², the region is bounded by a hyperbola with its center at the origin (0, 0) and its major axis along the x-axis. The hyperbola opens left and right. The inequality indicates that the region lies inside the hyperbola but does not include its boundary.

In the second inequality, 0 < y² - 4x², the region is bounded by a hyperbola with its center at the origin (0, 0) and its major axis along the y-axis. The hyperbola opens upward and downward. The inequality indicates that the region lies outside the hyperbola but does not include its boundary.

The solution to the system of inequalities is the intersection of the regions described by each inequality. Combining these two regions, we find that the solution is the area inside the first hyperbola (0 < 3x² - y²) but outside the second hyperbola (0 < y² - 4x²).

To summarize, the solution to the system of inequalities x² + y² < 4x² and y² - 4x² > 0 is the region inside the hyperbola x²/3 - y²/3 = 1.