Question

N(n+6)+9≤0 довести нерівність​

Answer 1

Ответ:

n(n+6)+9≤0

n²+6n+9≤0

(n+3)²≤0

(n+3)²=0

n²=-3²=-9

n=-3

Answer 2

To solve the inequality n(n+6) + 9 ≤ 0, we can start by expanding the equation:

n^2 + 6n + 9 ≤ 0.

Next, we can rewrite the equation in the form of a quadratic expression:

(n + 3)(n + 3) ≤ 0.

Now, to find the values of n that satisfy the inequality, we need to consider two scenarios:

1. When (n + 3) is positive: If (n + 3) > 0, then (n + 3)(n + 3) will also be positive. In this case, there are no solutions that satisfy the inequality.

2. When (n + 3) is negative or zero: If (n + 3) ≤ 0, then (n + 3)(n + 3) ≤ 0. This means that n + 3 must be less than or equal to zero. Solving for n, we get:

n + 3 ≤ 0 n ≤ -3.

So the solutions to the inequality n(n+6) + 9 ≤ 0 are all values of n less than or equal to -3.