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Omni-MATH / Initially, the number 1 and a non-integral number x are written on a blackboard. In each step, we can choose two numbers on the blackboard, not necessarily different, and write the…

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problem

Initially, the number 11 and a non-integral number xx are written on a blackboard. In each step, we can choose two numbers on the blackboard, not necessarily different, and write their sum or their difference on the blackboard. We can also choose a non-zero number of the blackboard and write its reciprocal on the blackboard. Is it possible to write x2x^2 on the blackboard in a finite number of moves?
Plain-text mathematical notation (without MathML)
Initially, the number 1 and a non-integral number x are written on a blackboard. In each step, we can choose two numbers on the blackboard, not necessarily different, and write their sum or their difference on the blackboard. We can also choose a non-zero number of the blackboard and write its reciprocal on the blackboard. Is it possible to write x² on the blackboard in a finite number of moves?
Original LaTeX notation
Initially, the number $1$ and a non-integral number $x$ are written on a blackboard. In each step, we can choose two numbers on the blackboard, not necessarily different, and write their sum or their difference on the blackboard. We can also choose a non-zero number of the blackboard and write its reciprocal on the blackboard. Is it possible to write $x^2$ on the blackboard in a finite number of moves?

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Source and history

task_id
91e60337-d3a1-5f2d-9d5d-881a047e948e
task_key
test--91e60337-d3a1-5f2d-9d5d-881a047e948e
task_revision_id
1
config / split
/ test

Official source

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