# How do you solve x^4-x^2+9<=0?

Jul 19, 2016

The Soln. does not exist, or,

The Soln. Set is $\phi$.

#### Explanation:

Given, ${x}^{4} = {x}^{2} \le - 9$

Completing the square on $L . H . S . , {x}^{4} - {x}^{2} + \frac{1}{4} \le - 9 + \frac{1}{4}$, i.e.,

${\left({x}^{2} - \frac{1}{2}\right)}^{2} \le - \frac{35}{4} < 0$, or,

${\left({x}^{2} - \frac{1}{2}\right)}^{2} < 0$, which is impossible in $\mathbb{R}$

Hence, the Soln. does not exist, or, in other words,

The Soln. Set is $\phi$.