Puzzles from Quanta

[Deleted member 4993]

1. Find the area of the triangle whose side lengths are 46, 85 and 38.

2. Let f (x) = 2x³ + bx² + cx + d. Find integers b, c and d such that f (1/4) = 0.

3. Find a perfect square, all of whose digits are in the set {2, 3, 7, 8}.

 

[Otis]

… from Quanta … the triangle whose side lengths are 46, 85 and 38 …

How can they say that?

 

[pka]

1. Find the area of the triangle whose side lengths are 46, 85 and 38.

How can they say that?

The triangle inequality?

 

[Deleted member 4993]

Did you try to use Heron's formula?

 

[pka]

Did you try to use Heron's formula?

No because \(46+38<85\) SEE HERE

 

[Otis]

The triangle inequality?

You must have misread my question.

\(\;\)

 

[pka]

You must have misread my question.

I certainly did not. Did you must not know about the triangle inequality??

 

[Dr.Peterson]

That's a rather diverse set of problems to all have the same answer.

 

[lookagain]

That's a rather diverse set of problems to all have the same answer.

Spoiler

"no solution" for all three problems

for the answers

 

[Deleted member 4993]

I certainly did not. Did you must not know about the triangle inequality??

Otis actually applied Cauchy-Schawartz inequality.

 

[Otis]

That's a rather diverse set of problems to all have the same answer.

I'd recognized the same answer for 3 as for 1 (by inspection), so I'd presumed 2 would turn out the same.

Shame on Quanta, if they unconditionally assigned those as puzzles. (Denis used to play the same trick.)

?

 

[Otis]

Otis actually applied Cauchy-Schawartz inequality.

Actually, I had not. But, that seems like a good suggestion because my psyche is a continuous function with respect to the mental landscape induced by my psyche itself.

 

[Otis]

I certainly did not [misunderstand your question about how Quanta could assert the existence of such a triangle] …

Okay, if you say so.

\(\;\)