Question

(x+1)(x-4)+4>(x+2)(x-3)x

Answer 1

Х+1•х-4+4>х+2•х-3•х
2х-8>3х-3х
2х-8>0

Answer 2

Let's solve the given inequality step by step:

(x + 1)(x - 4) + 4 > (x + 2)(x - 3)x

Expanding the expressions on both sides:

(x^2 - 3x - 4) + 4 > (x^2 - x - 6)x

Simplifying further:

x^2 - 3x > x^3 - x^2 - 6x

Rearranging terms and setting the inequality to zero:

x^3 - x^2 - 6x - x^2 + 3x + 6x > 0

Combining like terms:

x^3 - 2x^2 + 3x > 0

Now, we can factor the expression:

x(x^2 - 2x + 3) > 0

The quadratic equation x^2 - 2x + 3 does not factor nicely, so we can use the quadratic formula to find its roots:

x = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = 1, b = -2, and c = 3. Substituting the values into the formula:

x = (2 ± √((-2)^2 - 4(1)(3))) / (2(1)) x = (2 ± √(4 - 12)) / 2 x = (2 ± √(-8)) / 2

Since the discriminant (b^2 - 4ac) is negative, there are no real solutions for this quadratic equation. Therefore, the expression x^2 - 2x + 3 is always positive, and the inequality becomes:

x(x^2 - 2x + 3) > 0

Since the product of two numbers is greater than zero only when both numbers have the same sign (either both positive or both negative), we need to consider two cases:

1. x > 0: In this case, the inequality holds true when x > 0.

2. x < 0: In this case, the inequality holds true when x < 0.

Therefore, the solution to the given inequality is:

x > 0 or x < 0