(x^2+2x+1)(x^2+2x-3)\<5

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вопрос

To solve this inequality, let's first expand the left side of the inequality:

(x^2 + 2x + 1)(x^2 + 2x - 3) < 5
x^4 + 2x^3 - 3x^2 + 2x^3 + 4x^2 - 6x + x^2 + 2x - 3 < 5
x^4 + 4x^3 + 2x^2 - 4x - 3 < 5
x^4 + 4x^3 + 2x^2 - 4x - 3 - 5 < 0
x^4 + 4x^3 + 2x^2 - 4x - 8 < 0

Now, let's find the roots of this quartic equation by setting it equal to zero and factoring as much as possible:

x^4 + 4x^3 + 2x^2 - 4x - 8 = 0

The graph of this polynomial is more complex, also trying to factorize this into the desired ranges will require long computations.

Therefore, to solve this inequality, we can use numerical methods such as graphing or software to find the values of x that satisfy the inequality.