Find and such that they satisfy the constraints above. Submit your answer as .
If you think there are no and satisfying these equations, enter 123456 as your answer.
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I agree that x and y should be positive reals. Note that by AM-GM Inequality x y ≤ ( 2 x + y ) 2 ≤ 4 1 x 2 + y 2 = ( x + y ) 2 − 2 x y ≤ 1 2 − 2 ∗ 4 1 = 2 1 with equality when x = y = 2 1
1 0 = x y 2 + x 2 + y 2 1 ≥ 4 1 2 + 2 1 1 = 1 0 ⇒ x = y = 2 1
Hence ∣ x + y ∣ = 1