SOLUTION: Find two real numbers that have a sum of 8 and a product of 2.

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Question 182230: Find two real numbers that have a sum of 8 and a product of 2.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x and y be the two numbers, then:
1) x%2By+=+8 and
2) x%2Ay+=+2 Rewrite equation 1) as: x+=+8-y and substitute into equation 2).
2a) %288-y%29%2Ay+=+8 Simplify.
2a) 8y-y%5E2+=+8 Rewrite this in standard quadratic form.
y%5E2-8y%2B8+=+0 Solve by the quadratic formula:+y=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a where: a = 1, b = -8, and c = 2.
y+=+%28-%28-8%29%2B-sqrt%28%28-8%29%5E2-4%281%29%282%29%29%29%2F2%281%29 Evaluate.
y+=+%288%2B-sqrt%2864-8%29%29%2F2
y+=+%288%2B-sqrt%2856%29%29%2F2
highlight%28y+=+4%2Bsqrt%2814%29%29 or highlight%28y+=+4-sqrt%2814%29%29 These are the two real numbers.
Check:
x%2By+=+8 Substitute x+=+4%2Bsqrt%2814%29 and y+=+4-sqrt%2814%29
%284%2Bsqrt%2814%29%29%2B%284-sqrt%2814%29%29+=+8%2Bsqrt%2814%29-sqrt%2814%29 = 8
x%2Ay+=+2 Substitute for x and y as above.
%284%2Bsqrt%2814%29%29%2A%284-sqrt%2814%29%29+=+16-%28sqrt%2814%29%29%2A%28sqrt%2814%29%29 = 16-14+=+2