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Omni-MATH / A game involves jumping to the right on the real number line. If a and b are real numbers and b>a, the cost of jumping from a to b is b³−ab². For what real numbers c can one travel…

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problem

A game involves jumping to the right on the real number line. If aa and bb are real numbers and b>ab > a, the cost of jumping from aa to bb is b3−ab2b^3-ab^2. For what real numbers cc can one travel from 00 to 11 in a finite number of jumps with total cost exactly cc?
Plain-text mathematical notation (without MathML)
A game involves jumping to the right on the real number line. If a and b are real numbers
and b>a, the cost of jumping from a to b is b³−ab². For what real numbers
c can one travel from 0 to 1 in a finite number of jumps with total cost exactly c?
Original LaTeX notation
A game involves jumping to the right on the real number line. If $a$ and $b$ are real numbers
and $b > a$, the cost of jumping from $a$ to $b$ is $b^3-ab^2$. For what real numbers
$c$ can one travel from $0$ to $1$ in a finite number of jumps with total cost exactly $c$?

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Source and history

task_id
75df8e32-5e2e-51b2-82e3-258a7fb30d9d
task_key
test--75df8e32-5e2e-51b2-82e3-258a7fb30d9d
task_revision_id
1
config / split
/ test

Official source

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