- #1
whkoh
- 29
- 0
Solve for x in terms of a, the inequality:
[tex]
\mid x^2 - 3ax + 2a^2 \mid < \mid x^2 + 3ax - a^2 \mid
[/tex]
where [itex] x \in \mathbb{R}, a \in \mathbb{R}, a \neq 0[/itex]
Squaring both sides, I get
[tex]x^4 - 6ax^3 + 13a^2 x^2 - 12a^3 x + 4a^4 < x^4 + 6ax^3 + 7a^2 x^2 - 6a^3 x + a^4[/tex]
[tex]12ax^3 - 6a^2 x^2 + 6a^3 x - 3a^4 > 0[/tex]
[tex]4 ax^3 - 2a^2 x^2 + 2a^3 x - a^4 > 0[/tex]
Stuck here. How do I proceed?
[tex]
\mid x^2 - 3ax + 2a^2 \mid < \mid x^2 + 3ax - a^2 \mid
[/tex]
where [itex] x \in \mathbb{R}, a \in \mathbb{R}, a \neq 0[/itex]
Squaring both sides, I get
[tex]x^4 - 6ax^3 + 13a^2 x^2 - 12a^3 x + 4a^4 < x^4 + 6ax^3 + 7a^2 x^2 - 6a^3 x + a^4[/tex]
[tex]12ax^3 - 6a^2 x^2 + 6a^3 x - 3a^4 > 0[/tex]
[tex]4 ax^3 - 2a^2 x^2 + 2a^3 x - a^4 > 0[/tex]
Stuck here. How do I proceed?
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