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7. Determine a Pythagorean triple using the Babylonian formula. 1/m + 1/(m + 2) = a/b and c^2 = a^2 + b^2. Find a, b and c of the Pythagorean triple if m= 6.

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Answer:Explained

Explanation:

Given


(1)/(m)+(1)/(m+2)=(a)/(b)

and
c^2=a^2+b^2

For m =6


(1)/(6)+(1)/(8)=(a)/(b)


(7)/(24)=(a)/(b)


a=(7b)/(24)


c^2=\left [ (7^2)/(24^2) \right ]b^2+b^2


c=(25b)/(24)

Triplets are
\left ( a,b,c\right )


\left ( 7,24,25\right )


\left ( 14,48,50\right )


\left ( 21,72,75\right )

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