SOLUTION: Find two numbers (exactly) whose product is 54 and whose sum is 23.

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Question 362359: Find two numbers (exactly) whose product is 54 and whose sum is 23.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let A and B be the two numbers.
1.A%2AB=54
2.A%2BB=23%7D%7D%0D%0AFrom+eq.+2%2C%0D%0A%7B%7B%7BA=23-B
Substitute into eq. 1,
%2823-B%29B=54
23B-B%5E2=54
B%5E2-23B%2B54=0
Use the quadratic formula,
B+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
B+=+%2823+%2B-+sqrt%28+%28-23%29%5E2-4%2A1%2A%2854%29+%29%29%2F%282%2A1%29+
highlight%28B+=+%2823+%2B-+sqrt%28+313%29%29%2F%282%29%29+
Then
A%2BB=23
A%2B%2823+%2B-+sqrt%28313%29%29%2F2=46%2F2
A=%2823+%2B-+sqrt%28313%29%29%2F2
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(A,B)=(%2823+-+sqrt%28313%29%29%2F2,%2823+%2B+sqrt%28313%29%29%2F2)
and
(A,B)=(%2823+%2B+sqrt%28313%29%29%2F2,%2823+-+sqrt%28313%29%29%2F2)