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Omni-MATH / Over all real numbers x and y such that x³=3x+y and y³=3y+x compute the sum of all possible values of x²+y².

Problem

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problem

Over all real numbers xx and yy such that x3=3x+y and y3=3y+xx^{3}=3 x+y \quad \text { and } \quad y^{3}=3 y+x compute the sum of all possible values of x2+y2x^{2}+y^{2}.
Plain-text mathematical notation (without MathML)
Over all real numbers x and y such that x³=3x+y  and  y³=3y+x compute the sum of all possible values of x²+y².
Original LaTeX notation
Over all real numbers $x$ and $y$ such that $$x^{3}=3 x+y \quad \text { and } \quad y^{3}=3 y+x$$ compute the sum of all possible values of $x^{2}+y^{2}$.

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Source and history

task_id
b25ed77a-579c-522c-a3c3-b4becd4fd4c5
task_key
test--b25ed77a-579c-522c-a3c3-b4becd4fd4c5
task_revision_id
1
config / split
/ test

Official source

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