How do you solve #x^4<4x^2#?
1 Answer
i.e.
Explanation:
First note that if
If
#x^2 < 4#
Case
Since
#x < 2#
Hence we have solutions:
#0 < x < 2#
Case
Note that
#-x < 2#
Multiplying both sides by
#x > -2#
Hence we have solutions:
#-2 < x < 0#
Background
The truth or falsity of an inequality is unaltered by any of the following operations:
- Add or subtract the same value from both sides.
- Multiply or divide both sides by the same positive value.
- Multiply or divide both sides by the same negative value and reverse the inequality (
#<# becomes#># ,#>=# becomes#<=# , etc.).
More generally:
- Apply the same strictly monotonically increasing function to both sides of the inequality.
- Apply the same strictly monotonically decreasing function to both sides of the inequality and reverse the inequality.