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#1 2023-08-20 01:12:20

Math Enthusiast
Registered: 2023-08-20
Posts: 1

Proving a side of a triangle is a cube.

Hello guys,

I have tried different approaches and can't get to the solution. Your help is very much appreciated. TIA!

How do I prove that at least of the sides p, q, r is a cube given the following: the side lengths p, q, r of a triangle PQR are positive integers such that the highest common factor of p, q, and r is 1 and that angle P = 3Q?


#2 2023-08-21 21:16:10

Registered: 2010-06-20
Posts: 10,472

Re: Proving a side of a triangle is a cube.

hi Math Enthusiast

Just want to check I'm understanding the problem.

A triangle PQR with sides p, q, r (convention is p is opposite P etc)

Angle at P is 3Q => angle at R is 180 - 4Q

p, q, and r are all integers.

HCF(p, q, r) = 1

Find smallest side which is a perfect cube number {1, 8, 27, 64,.....}

Is that it?


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