To solve this inequality, we need to simplify both sides and then find the values of x that satisfy the inequality.
Starting with the left side of the inequality:
H³ - 3x² + 2x - 6
This can be simplified to:
H³ - 2x² + 2x - 6
Now simplifying the right side of the inequality:
2x² - x² + x⁴ - 2
This simplifies to:
x⁴ + x² - 2
Therefore, the inequality becomes:
H³ - 2x² + 2x - 6 > x⁴ + x² - 2
Combining like terms, we get:
-x⁴ - 3x² + 2x - 4 > 0
Now we need to find the values of x that satisfy this inequality. This is a quadratic inequality, so we can find the critical points by setting the expression equal to zero:
-x⁴ - 3x² + 2x - 4 = 0
We can solve this equation to find the critical points. Once we have the critical points, we can test a value in each interval to determine which intervals satisfy the inequality.
I hope this helps! Let me know if you need further assistance.
To solve this inequality, we need to simplify both sides and then find the values of x that satisfy the inequality.
Starting with the left side of the inequality:
H³ - 3x² + 2x - 6
This can be simplified to:
H³ - 2x² + 2x - 6
Now simplifying the right side of the inequality:
2x² - x² + x⁴ - 2
This simplifies to:
x⁴ + x² - 2
Therefore, the inequality becomes:
H³ - 2x² + 2x - 6 > x⁴ + x² - 2
Combining like terms, we get:
-x⁴ - 3x² + 2x - 4 > 0
Now we need to find the values of x that satisfy this inequality. This is a quadratic inequality, so we can find the critical points by setting the expression equal to zero:
-x⁴ - 3x² + 2x - 4 = 0
We can solve this equation to find the critical points. Once we have the critical points, we can test a value in each interval to determine which intervals satisfy the inequality.
I hope this helps! Let me know if you need further assistance.