Question

Find the number of integers satisfying these inequality
${x}^{2} + 6x - 7≤2$
​

Answer 1

Answer:

x  

4

−5x  

2

+4≤0

⇒x  

4

−4x  

2

−x  

2

+4≤0

⇒x  

2

(x  

2

−4)−1(x  

2

−4)≤0

⇒(x  

2

−4)(x  

2

−1)≤0

⇒(x−2)(x+2)(x−1)(x+1)≤0

The critical points are {−2,−1,1,2}∈Z

Hence numbers of integers satisfying the inequalities=4

(ii)x  

4

−2x  

2

+63≤0

⇒x  

4

−2x  

2

+1−1+63≤0

⇒(x  

2

−1)  

2

+62≤0

⇒(x  

2

−1)  

2

+≤−62

⇒x  

2

−1≤±  

−62

​

 

Thus, there exists no integer.Hence numbers of integers satisfying the inequalities= 0