The difference between two integers is 6. The sum of their sqaures is a minimum. Find the 2 integers. Answer with explanation gets brainliest.
Mathematics
AaryamanKumar
Question
The difference between two integers is 6. The sum of their sqaures is a minimum. Find the 2 integers.
Answer with explanation gets brainliest.
Answer with explanation gets brainliest.
1 Answer

1. User Answers mhanifa
Answer:
 3 and  3
Stepbystep explanation:
Let the numbers are x and y.
Their difference is:
 x  y = 6
Sum of their squares:
 S = x² + y²
Substitute y = x  6 into sum equation:
 S = x² + (x  6)² =
 x² + x²  12x + 36 =
 2x²  12x + 36
We observe this is a quadratic expression. It has minimum value at vertex, which is when x = b/2a or:
 x =  (12/2*2) = 3
Then the value of y is:
 y = x  6 = 3  6 =  3