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

Step-by-step explanation:

Given

$\frac{1}{m}+\frac{1}{m+2}=\frac{a}{b}$

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

For m =6

$\frac{1}{6}+\frac{1}{8}=\frac{a}{b}$

$\frac{7}{24}=\frac{a}{b}$

$a=\frac{7b}{24}$

$c^2=\left [ \frac{7^2}{24^2} \right ]b^2+b^2$

$c=\frac{25b}{24}$

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

$\left ( 7,24,25\right )$

$\left ( 14,48,50\right )$

$\left ( 21,72,75\right )$