Question

1)у=√х и у=√-х2)у=2√х и у=√2х3)у=√х и у= -√ч

Answer 1

Y=✓x первоє
y=2✓x втрроє
y=✓x третеє

Answer 2

Let's analyze each pair of equations one by one:

1. у = √x and у = √(-x)

The first equation, у = √x, represents the upper half of the graph of the square root function, where y is non-negative (assuming x is non-negative as well).

The second equation, у = √(-x), represents the upper half of the graph of the square root of the negative value of x. However, this equation has no real solutions for y since the square root of a negative number is not a real number. Therefore, there is no overlap between the graphs of the two equations. The graphs are separate, and there is no common solution.

2. у = 2√x and у = √2x

The first equation, у = 2√x, represents the upper half of the graph of the square root function scaled vertically by a factor of 2.

The second equation, у = √2x, represents the upper half of the graph of the square root function, where x is multiplied by 2 before taking the square root.

These two equations may or may not have a common solution, depending on the value of x. To find the common solution, we need to equate the two expressions:

2√x = √2x

To solve for x, we can square both sides of the equation:

(2√x)^2 = (√2x)^2

4x = 2x

Now, subtract 2x from both sides:

4x - 2x = 0

2x = 0

Divide both sides by 2:

x = 0

So, the common solution for these two equations is x = 0.

3. у = √x and у = -√x

The first equation, у = √x, represents the upper half of the graph of the square root function, where y is non-negative.

The second equation, у = -√x, represents the lower half of the graph of the square root function, where y is non-positive.

Again, these two equations have no common solution since they represent different parts of the graph of the square root function. The graphs are separate and do not intersect.

In summary:

1. No common solution.
2. The common solution is x = 0.
3. No common solution.