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Chapter 4: Q. 29 (page 242)

Solve the inequality algebraically.

x4>x2

Short Answer

Expert verified

The required interval set is :

(-鈭�,-1)鈭�(1,鈭�)

Step by step solution

01

Step 1. Given inequality 

x4>x2

02

Step 2. Factorization

x4>x2x4-x2>0x2(x2-1)>0x2(x+1)(x-1)>0

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

03

Step 3. Dividing the number line into 4 intervals 

(-鈭�,-1)(-1,0)(0,1)(1,鈭�)

These are the intervals

04

Step 4. Evaluating the value of function at different intervals

1.(-鈭�,-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,鈭�)

Let us take 2

the value of the function at2=12

the condition is satisfied.

4.(0,1)

Let us take 0.1

the value of the function at0.1=-0.0099

the condition is not satisfied.

05

Step 5. Conclusion

The required interval set is :

(-鈭�,-1)鈭�(1,鈭�)

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