Question

Решите систему неравенств 1/х<х х+2>=0 Заранее Спасибо!

Answer 1

Давно не решал, не уверен в ответе на 100%

Answer 2

Solving the System of Inequalities

To solve the system of inequalities 1/x < x and x + 2 > 0, we will break it down into two separate inequalities and find the solution for each one.

# Inequality 1: 1/x < x

To solve the inequality 1/x < x, we can start by multiplying both sides of the inequality by x. However, since x can be positive or negative, we need to consider both cases separately.

Case 1: x > 0

If x > 0, we can multiply both sides of the inequality by x without changing the direction of the inequality:

1/x < x

Multiplying both sides by x:

1 < x^2

Taking the square root of both sides:

1 < x

So, for x > 0, the solution to the inequality 1/x < x is 1 < x.

Case 2: x < 0

If x < 0, we need to multiply both sides of the inequality by x, which reverses the direction of the inequality:

1/x < x

Multiplying both sides by x:

1 > x^2

Taking the square root of both sides:

1 > x

So, for x < 0, the solution to the inequality 1/x < x is x < 1.

# Inequality 2: x + 2 > 0

To solve the inequality x + 2 > 0, we can subtract 2 from both sides:

x > -2

So, the solution to the inequality x + 2 > 0 is x > -2.

# Combining the Solutions

Now that we have found the solutions for each inequality, we can combine them to find the overall solution for the system of inequalities.

For x > 0, the solution is 1 < x.

For x < 0, the solution is x < 1.

For x > -2, the solution is x > -2.

Therefore, the overall solution for the system of inequalities 1/x < x and x + 2 > 0 is:

x < 1 or x > -2.

Please note that the solution is expressed in interval notation.