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

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Question 197327: Find two real numbers that have a sum of 8 and a product of 2.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Find two real numbers: x and y:
:
that have a sum of 8
x + y = 8
y = (8-x); use for substitution
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and a product of 2.
x*y = 2
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Replace y with (8-x) in the above equation:
x(8-x) = 2
:
8x - x^2 = 2
:
-x^2 + 8s - 2 = 0
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Use the quadratic formula to find x
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation; a=-1; b=8; c=-2
x+=+%28-8+%2B-+sqrt%288%5E2+-+4+%2A+-1+%2A+-2+%29%29%2F%282%2A-1%29+
:
x+=+%28-8+%2B-+sqrt%2864+-+8+%29%29%2F%28-2%29+
:
x+=+%28-8+%2B-+sqrt%2856+%29%29%2F%28-2%29+
Two solutions:
x+=+%28-8+%2B+7.4833%29%2F%28-2%29+
:
x+=+%28-.5167%29%2F%28-2%29+
x = +.258; then y =7.742
and
x+=+%28-8+-+7.4833%29%2F%28-2%29+
:
x+=+%28-15.4833%29%2F%28-2%29+
x = +7.742; then y = .258
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You can check these solutions in the original problem