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MATH / If arccosx+arccos2x+arccos3x=π, then x satisfies a cubic polynomial of the form ax³+bx²+cx+d=0,where a, b, c, and d are integers, and a≠0. Find the smallest possible value of …

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problem

If arccosx+arccos2x+arccos3x=π,\arccos x + \arccos 2x + \arccos 3x = \pi, then xx satisfies a cubic polynomial of the form ax3+bx2+cx+d=0,ax^3 + bx^2 + cx + d = 0,where a,a, b,b, c,c, and dd are integers, and a≠0.a \neq 0. Find the smallest possible value of |a|+|b|+|c|+|d|.|a| + |b| + |c| + |d|.
Plain-text mathematical notation (without MathML)
If arccosx+arccos2x+arccos3x=π, then x satisfies a cubic polynomial of the form
ax³+bx²+cx+d=0,where a, b, c, and d are integers, and a≠0.  Find the smallest possible value of |a|+|b|+|c|+|d|.
Original LaTeX notation
If $\arccos x + \arccos 2x + \arccos 3x = \pi,$ then $x$ satisfies a cubic polynomial of the form
\[ax^3 + bx^2 + cx + d = 0,\]where $a,$ $b,$ $c,$ and $d$ are integers, and $a \neq 0.$  Find the smallest possible value of $|a| + |b| + |c| + |d|.$

level

Level 5

type

Precalculus

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Source and history

task_id
7f11fc60-d66c-5f8d-977a-c3cb601adf6b
task_key
precalculus--test--7f11fc60-d66c-5f8d-977a-c3cb601adf6b
task_revision_id
1
config / split
precalculus / test

Official source

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