Question

Solve the inequality algebraically

$(x-5{)}^2(x+2)>0$

Short answer

Required solution set is $(-2,5)\cup (5,\infty )$.

Step-by-step solution

Step 1. Given information  

We are given an inequality,

$(x-5{)}^2(x+2)>0$

Step 2.Finding the zeros   

The zeros of inequality $(x-5{)}^2(x+2)>0$are,

$5$and$-2$

So, the intervals will be,

role="math" localid="1646300391442" $(-\infty ,-2),(-2,5)\text{and}(5,\infty )$

Step 4. Selecting a test number in each interval  

The table is as follows,

Hence the solution set is $(-2,5)\cup (5,\infty )$.