perplexus.info :: Just Math : From a to z

From a to z (Posted on 2022-04-17)

If a=31,415,926,535³-31,415,926,533³

Evaluate z=sqrt((a-2)/6)

No Solution Yet Submitted by Ady TZIDON

Rating: 4.5000 (2 votes)

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Puzzle Solution

| Comment 1 of 7

Let b=31,415,926,533 (say)

Then, we must hae:

a= (b+2)^3 -b^3

= 3*(b^2) *2+ 3*b*(2)^2+2^3

= 6*b^2 +12*b +8

So, a-2 = 6*b^2 +12*b +6

=6*(b+1)^2

=> (a-2)/6 = (b+1)^2

=> V[(a-2)/6] = b+1

So, z= b+1 = 31,415,926,534

*** As 3.1415926535 is close to pi - how one wishes that this puzzle was published on a Pi Day !!!

[/EDIT /] : Actually 3.1415926536 is CLOSER to pi than the abovementioned number.

Edited on April 17, 2022, 7:25 am

Posted by K Sengupta on 2022-04-17 07:03:51

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