Question

The sum of the squares of two numbers is 2. The product of the two numbers is 1. Find the numbers.

xy=1
x^2+y^2=2

x^4+1=2x^2
x^4-2x^2+1=0

I don't think you can factor that
unless its (x^2+1)(x^2-1)

but I don't know where to go from there

Answer 1

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x^4-2x^2+1=0

I don't think you can factor that
unless its (x^2+1)(x^2-1)
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If you FOIL that, you will get x^4 - 1, not x^4 - 2x^2 + 1.

You can factor by grouping
x^4 - 2x^2 + 1 = 0
x^4 - (x^2 + x^2) + 1 = 0
x^4 - x^2 - x^2 + 1 = 0
x^2(x^2 - 1) + -1(x^2 - 1) = 0
(x^2 - 1)(x^2 - 1) = 0
x^2 = 1
x = 1