Question

How many integers satisfy the inequality (x 2 – 4)(x 2 – 10) < 0?

Answer 1

Answer:

There are 2 integers

Step-by-step explanation:

Answer 2

Answer:

2 integers (2 and -2)

Step-by-step explanation:

Given the inequality (x²– 4)(x² – 10) < 0, we are to find the number of integers that satisfies the inequality

From (x²– 4)(x² – 10) < 0, (x²– 4)< 0 and (x² – 10) < 0

For (x²– 4)< 0;

x²<4

take the square root of both sides;

√x²<√4

x < ±2

x<2 and x<-2

Similarly for (x²– 10)< 0;

x²<10

take the square root of both sides;

√x²<±√10

x < ±√10

x<√10 and x<-√10

Note that √10 is not an integer but an irrational number. An integer should be a negative or positive whole number. Therefore the amount of integers that satisfies the equation is 2 i.e 2 and -2