Question

question 38 points 2 the product of two consecutive positive even integers is 48. find the greatest positive integer. 8 12 24 48

Explanation:

Step1: Define the integers

Let the smaller even integer be $x$, the larger one is $x+2$.

Step2: Set up the equation

$x(x+2)=48$
Expand: $x^2+2x-48=0$

Step3: Solve the quadratic equation

Factor: $(x+8)(x-6)=0$
Solutions: $x=-8$ or $x=6$

Step4: Select positive integer

We take $x=6$, so the larger integer is $6+2=8$.

Answer:

O 8