SOLUTION: What 2 numbers add to get "1" and multiply to get "5"?

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Question 1050872: What 2 numbers add to get "1" and multiply to get "5"?
Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
1) x + y = 1
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2) x * y = 5
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solve equation 1) for x
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x = 1 - y
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substitute for x in equation 2)
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(1 - y) * y = 5
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y - y^2 = 5
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y^2 -y +5 = 0
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solve for y by completing the square
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y^2 -y = -5
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y^2 -y +(1/4) = -5 +(1/4)
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(y - (1/2))^2 = -19/4
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y -(1/2) = square root(-19/4) = (i * square root(19))/2
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**********************************
y = (1 + i * square root(19)) / 2
y = (1 - i * square root(19)) / 2
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***********************************************************************
x = 1 - ((1 + i * square root(19)) / 2) = (1 - i * square root(19)) / 2
x = 1 - ((1 - i * square root(19)) / 2) = (1 + i * square root(19)) / 2
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we have two sets of solutions
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x = (1 - i * square root(19)) / 2
y = (1 + i * square root(19)) / 2
:
x = (1 + i * square root(19)) / 2
y = (1 - i * square root(19)) / 2
**********************************
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checking answers
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clearly x + y = 1
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what about xy = 5
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xy = (1 -(i^2 * 19)) / 4 = (1 - (-19)) / 4 = 20 / 4 = 5
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our answers check :-)
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