SOLUTION: The sum of the squares of two numbers is 4 and the product of them is 1. Find the two numbers. I think that the two simultanious equations are Let the numbers be x and y x(sq

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Question 765632: The sum of the squares of two numbers is 4 and the product of them is 1. Find
the two numbers.
I think that the two simultanious equations are
Let the numbers be x and y
x(square) + y(square) = 4
xy = 1
But the answer is a decimal... and it doesn't fit the two equations... please help me
Thanks
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x(square) + y(square) = 4
xy = 1
-------
Solve for "y":
y = 1/x
----
Substitute for "y" and solve for "x":
x^2 + (1/x)^2 = 4
----
x^4 + 1 = 4x^2
------------
x^4 - 4x^2 + 1 = 0
----
x^2 = [4 +- sqrt(16-4)]/2
---
x^2 = [4+- 2sqrt(3)]/2
--
x^2 = 2 +- sqrt(3)
----
x = sqrt[2+sqrt(3)] or x = -sqrt[2+sqrt(3)]
----
Solve for "y"
y = 1/sqrt[2+sqrt(3)] or y = -1/sqrt[2+sqrt(3)]
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Cheers,
Stan H.
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