Chapter 4: Q. 29 (page 242)

Solve the inequality algebraically.
$x^{4} > x^{2}$

Short Answer

Expert verified

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

$x^{4} > x^{2} x^{4} - x^{2} > 0 x^{2} (x^{2} - 1) > 0 x^{2} (x + 1) (x - 1) > 0$

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

Step 3. Dividing the number line into 4 intervals

$(- \infty, - 1) (- 1, 0) (0, 1) (1, \infty)$

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 :

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

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Solve the inequality algebraically.
$x^{4} > x^{2}$

Short Answer

Step by step solution

Step 1. Given inequality

Step 2. Factorization

Step 3. Dividing the number line into 4 intervals

Step 4. Evaluating the value of function at different intervals

Step 5. Conclusion

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Solve the inequality algebraically.x4>x2

Short Answer

Step by step solution

Step 1. Given inequality

Step 2. Factorization

Step 3. Dividing the number line into 4 intervals

Step 4. Evaluating the value of function at different intervals

Step 5. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

Logic and Functions

Discrete Mathematics

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

Solve the inequality algebraically.
$x^{4} > x^{2}$