SOLUTION: Does anyone know how to go about this problem? The difference of two positive numbers is 3 and the sum of their squares is 65. Find the numbers.

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Question 214333: Does anyone know how to go about this problem? The difference of two positive numbers is 3 and the sum of their squares is 65. Find the numbers.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
let the numbers be j and k
given:
(1) k+-+j+=+3
(2) j%5E2+%2B+k%5E2+=+65
From (1),
k+=+j+%2B+3
j%5E2+%2B+%28j+%2B+3%29%5E2+=+65
j%5E2+%2B+j%5E2+%2B+6j+%2B+9+=+65
2j%5E2+%2B+6j+-+56+=+0
j%5E2+%2B+3j+-+28+=+0
solve using quadratic equation
j+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+3
c+=+-28
j+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-28%29+%29%29%2F%282%2A1%29+
j+=+%28-3+%2B-+sqrt%28+9+%2B+112+%29%29%2F2+
j+=+%28-3+%2B-+sqrt%28+121+%29%29%2F2+
j+=+%28-3+%2B+11%29%2F2
j+=+4
and
j+=+%28-3+-+11%29%2F2
j+=+-7 (can't use negative result)
k+=+j+%2B+3
k+=+7
The numbers are 4 and 7
check:
(2) j%5E2+%2B+k%5E2+=+65
4%5E2+%2B+7%5E2+=+65
16+%2B+49+=+65
65+=+65 OK