Question

Solve the inequality algebraically.

$x^4>x^2$

Short answer

The required interval set is :

$(-\infty ,-1)\cup (1,\infty )$

Step-by-step solution

Step 1. Given inequality 

$x^4>x^2$

Step 2. Factorization

$$\begin{gathered} x^4>x^2 \\ {x}^4-x^2>0 \\ {x}^2(x^2-1)>0 \\ {x}^2(x+1)(x-1)>0 \end{gathered}$$

The zeros of the above equation are : 0,1,-1

Step 3. Dividing the number line into 4 intervals 

$$\begin{gathered} (-\infty ,-1) \\ (-1,0) \\ (0,1) \\ (1,\infty ) \end{gathered}$$

These are the intervals

Step 4. Evaluating the value of function at different intervals

1.$(-\infty ,-1)$

Let us take$-2$

the value of the function at $-2=12$

the condition is satisfied.

2.$(-1,0)$

Let us take$-0.1$

the value of the function at $-0.1=-0.0099$

the condition is not satisfied.

3.$(1,\infty )$

Let us take $2$

the value of the function at$2=12$

the condition is satisfied.

4.$(0,1)$

Let us take $0.1$

the value of the function at$0.1=-0.0099$

the condition is not satisfied.

Step 5. Conclusion

The required interval set is :

$(-\infty ,-1)\cup (1,\infty )$