IN A PYTHAGOREAN TRIPLET ONE OF ITS MEMBER IS 13 ,FIND THE OTHERS
Three numbers are said to be Pythagorean triplet, if they satisfy the Pythagoras theorem.
We may get Pythagorean triplets by using general formula 2m, m2 – 1, m2 + 1 ,where m is a natural number.
Let m2 – 1 = 13
⇒ m2 = 14
The value of m will not be an integer.
We try to take m2 + 1 = 13
⇒ m2 = 12
Again, we will not get an integer value of m.
Now, we take 2m = 13
We will again not get an integer value of m.
We may observe that not all the triplets may be obtained using the above method.
See 5, 12 and 13 are triplet having 13 as its member, but it could not be obtained by using above method. [132 = 52 + 122]