Question

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.

Answer 1

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 )`