The idea of principal component method can be used to solve this problem.

Take x as the main element, and arrange it to get

x？ +2yx+2y？ - 1=0

This equation has a real root (otherwise x can't get a value).

δ= 4y？ -4(2y？ - 1)

=4y？ -8y？ +4

=4-4y？ ≥0

y？ ≤ 1

So - 1≤y≤ 1

The minimum value of y is-1, which is obtained when x= 1.

The maximum value of y is 1, which is obtained when x=- 1.

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