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MATH / The equation

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

The equation 4cos27∘=a+b+c−d4 \cos 27^\circ = \sqrt{a + \sqrt{b}} + \sqrt{c - \sqrt {d}}holds for some positive integers a,a, b,b, c,c, and d,d, where bb is not divisible by the square of a prime, and dd is not divisible by the square of a prime. Find a+b+c+d.a + b + c + d.
Plain-text mathematical notation (without MathML)
The equation
4cos27^(∘)=√(a+√(b))+√(c−√(d))holds for some positive integers a, b, c, and d, where b is not divisible by the square of a prime, and d is not divisible by the square of a prime.  Find a+b+c+d.
Original LaTeX notation
The equation
\[4 \cos 27^\circ = \sqrt{a + \sqrt{b}} + \sqrt{c - \sqrt {d}}\]holds for some positive integers $a,$ $b,$ $c,$ and $d,$ where $b$ is not divisible by the square of a prime, and $d$ is not divisible by the square of a prime.  Find $a + b + c + d.$

level

Level 5

type

Precalculus

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Source and history

task_id
cb683f89-eb9e-545d-bcb9-1a3ee4b0748b
task_key
precalculus--test--cb683f89-eb9e-545d-bcb9-1a3ee4b0748b
task_revision_id
1
config / split
precalculus / test

Official source

initial import