One says that 10 is divided into three parts and if the small part is multiplied by itself and added to the middle one multiplied by itself the result is the large one multiplied by itself, and when the small part is multiplied by the large part, it equals the middle part multiplied by itself. Find the parts.

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Abu Kamil, Algebra (ca 900)

Abu Kamil, Algebra (ca 900)

Statement #1: 10 is divided into three parts

Giving .................................... x + y + z = 10

Statement #2: if the small part is multiplied by itself and added to the middle one multiplied by itself the result is the large one multiplied by itself

Giving ..................................... x^2 + y^2 = z^2

Statement #3: when the small part is multiplied by the large part, it equals the middle part multiplied by itself

Giving ..................................... x * y = z^2

Hint: The answer is: x = 2.57066; y = 3.26993; z = 4.15941

Show how you can find these results.

Statement #3 should maybe be x * z = y^2 ?

ReplyDeletePaul.