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
