Chapter 4: Q. 30 (page 242)

Solve the inequality algebraically.
$x^{4} < 9 x^{2}$

Short Answer

Expert verified

The required interval set is :

$(- 3, 3)$

Step by step solution

Step 1. Given inequality

$x^{4} < 9 x^{2}$

we need to solve for x.

Step 2. Factorization

$x^{4} - 9 x^{2} < 0 x^{2} (x^{2} - 9) < 0 x^{2} (x + 3) (x - 3) < 0$

The zeros of the given equation are :

$0, 3, - 3$ localid="1646130204622" $0, 3, - 3$

Step 3. Dividing the number line into 3 intervals

$(- \infty, - 3) (- 3, 3) (3, \infty)$

Step 4. Evaluating the value of function at different intervals

3. $(- \infty, - 3)$

let us take the value -4

the value of function at -4

$= 112$

2. $(- 3, 3)$

let us take the number 2

the value of the function at x=2 is :

$= - 20$

1. $(3, \infty)$

let us take the value 4

the value of function at x= 4

$= 112$

Step 5. Conclusion

The required interval set is :

(-3,3)

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Solve the inequality algebraically.
$x^{4} < 9 x^{2}$

Short Answer

Step by step solution

Step 1. Given inequality

Step 2. Factorization

Step 3. Dividing the number line into 3 intervals

Step 4. Evaluating the value of function at different intervals

Step 5. Conclusion

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Solve the inequality algebraically.x4<9x2

Short Answer

Step by step solution

Step 1. Given inequality

Step 2. Factorization

Step 3. Dividing the number line into 3 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

Statistics

Theoretical and Mathematical Physics

Decision Maths

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Solve the inequality algebraically.
$x^{4} < 9 x^{2}$