perplexus.info :: Just Math : Given Product Equaling 1, Find the Square

Given Product Equaling 1, Find the Square (Posted on 2024-04-24)

Let each of m and n be a real number that satisfy this equation:
(2m+√(1+ 4m²))(3n+√(1+9n²))=1

Determine the value of (2m+3n)²

No Solution Yet Submitted by K Sengupta

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a solution

| Comment 1 of 2

Case 1:

By inspection, m=n=0 is a solution.

Case2:

suppose 2m = -3n = k,

then both radicals are the same

(k + √(1+k^2))(-k + √(1+k^2))

-k^2 + (1+k^2) = 1

In both cases, (2m+3n)^2 = 0

I do not believe that I have proved this to be the only solution.

Posted by Larry on 2024-04-24 12:03:48

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