Solve the inequality. Write the solution set in interval notation.
-$$\left( x ^ { 2 } - 64 \right) \left( x ^ { 2 } - 25 \right) 0$$
A) $( - \infty , - 8 ] \cup [ - 5,5 ] \cup [ 8 , \infty )$
B) $( - \infty , - 8 ) \cup ( - 5,5 ) \cup ( 8 , \infty )$
C) $( - 8 , - 5 ) \cup ( 5,8 )$
D) $[ - 8 , - 5 ] \cup [ 5,8 ]$

Question

Solve the inequality. Write the solution set in interval notation.
-$$\left( x ^ { 2 } - 64 \right) \left( x ^ { 2 } - 25 \right) > 0$$
A) $( - \infty , - 8 ] \cup [ - 5,5 ] \cup [ 8 , \infty )$
B) $( - \infty , - 8 ) \cup ( - 5,5 ) \cup ( 8 , \infty )$
C) $( - 8 , - 5 ) \cup ( 5,8 )$
D) $[ - 8 , - 5 ] \cup [ 5,8 ]$

Quizplus · Accepted Answer

The inequality $(x^2 - 64)(x^2 - 25) > 0$ factors into $(x + 8)(x - 8)(x + 5)(x - 5) > 0$. The roots are $x = -8, -5, 5, 8$. The inequality is satisfied in intervals where the product is positive, which occurs between the roots and outside the outer roots, leading to the solution $(-\infty, -8) \cup (-5, 5) \cup (8, \infty)$.

Solve the Inequality (x2−64)(x2−25)>0\left( x ^ { 2 } - 64 \right) \left( x ^ { 2 } - 25 \right) > 0(x2−64)(x2−25)>0

Solve the Inequality $\left( x ^ { 2 } - 64 \right) \left( x ^ { 2 } - 25 \right) > 0$