Question

2 корень из 4 +5х + х^2 <= х +1

Answer 1

Let's begin by simplifying the left side of the inequality:

2√4 + 5x + x^2 = 2*2 + 5x + x^2 = x^2 + 5x + 4

So we can rewrite the inequality as:

x^2 + 5x + 4 <= x + 1

Moving all terms to the left side, we get:

x^2 + 4x + 3 <= 0

Now we can factor the left side of the inequality:

(x + 3)(x + 1) <= 0

To solve this inequality, we need to consider the sign of each factor and their product in the intervals defined by their roots, which are -3 and -1:

For x < -3, both factors are negative, so their product is positive. For -3 < x < -1, the factor (x+3) is positive and the factor (x+1) is negative, so their product is negative. For x > -1, both factors are positive, so their product is positive.

Therefore, the solution to the inequality is:

-3 <= x <= -1

So the values of x that satisfy the inequality are between -3 and -1, inclusive.