Answer:
The two numbers are 4 and 6
Step-by-step explanation:
Suppose we have:
x=The smallest even integer
x+2=Next even integer
Recall even numbers occur every other integer.
The condition of the problem states the square of the smaller integer is 10 more than the longer integer:
[tex]x^2=10+x+2[/tex]
Rearranging and simplifying:
[tex]x^2-x-12=0[/tex]
Factoring:
[tex](x-4)(x+3)=0[/tex]
We have two solutions:
x=4, x=-3
Since the integers must be positive:
x=4
Next even integer= x+2=6
The two numbers are 4 and 6
