Question

3x-x^2(15+x)>-(x+5)^3-4x

Answer 1

Уравнение не имеет корней.

Answer 2

To solve the inequality $3x - x^2(15+x) > -(x+5)^3 - 4x$, we need to find the values of $x$ that satisfy the inequality. Let's simplify the inequality step-by-step:

Step 1: Expand the terms on both sides of the inequality: $3x - x^2(15+x) > -(x+5)^3 - 4x$
$3x - (15x^2 + x^3) > - (x+5)(x+5)(x+5) - 4x$
$3x - 15x^2 - x^3 > - (x+5)^3 - 4x$
$-x^3 - 15x^2 + 3x > - (x+5)^3 - 4x$

Step 2: Move all terms to one side of the inequality: $-x^3 - 15x^2 + 3x + (x+5)^3 + 4x > 0$

Step 3: Combine like terms and expand the cube: $-x^3 - 15x^2 + 3x + (x^3 + 15x^2 + 75x + 125) + 4x > 0$
$-x^3 - 15x^2 + 3x + x^3 + 15x^2 + 75x + 125 + 4x > 0$

Step 4: Cancel out common terms: $3x + 75x + 125 > 0$
$78x + 125 > 0$

Step 5: Solve for $x$: Subtract 125 from both sides: $78x > -125$

Finally, divide both sides by 78 (remembering to flip the inequality sign when dividing by a negative number): $x < \frac{-125}{78}$

So the solution to the inequality is $x < \frac{-125}{78}$.