To solve the inequality:
(a^2 - 3) + 5a > a^3 + 2(a - 2)
First, simplify both sides of the inequality:
a^2 - 3 + 5a > a^3 + 2a - 4a^2 + 5a - 3 > a^3 + 2a - 4
Rearrange the terms to set the inequality to zero:
a^2 - 2a + 1 > 0(a - 1)^2 > 0
Since (a - 1)^2 is always positive for any real number a, the inequality is always satisfied. Therefore, the solution to the inequality is all real numbers.
In interval notation, the solution is (-∞, ∞).
To solve the inequality:
(a^2 - 3) + 5a > a^3 + 2(a - 2)
First, simplify both sides of the inequality:
a^2 - 3 + 5a > a^3 + 2a - 4
a^2 + 5a - 3 > a^3 + 2a - 4
Rearrange the terms to set the inequality to zero:
a^2 - 2a + 1 > 0
(a - 1)^2 > 0
Since (a - 1)^2 is always positive for any real number a, the inequality is always satisfied. Therefore, the solution to the inequality is all real numbers.
In interval notation, the solution is (-∞, ∞).