Step-by-step explanation:
Sure, a Pythagorean triplet consists of three positive integers a, b, and c such that \(a^2 + b^2 = c^2\).
Given that one member is 14, let's find the other two members of the triplet.
Let \(a = 14\).
The Pythagorean triplet is commonly written in the form \(a^2 + b^2 = c^2\), where \(a < b < c\).
Substituting \(a = 14\) into the Pythagorean equation:
\[14^2 + b^2 = c^2\]
\[196 + b^2 = c^2\]
We're looking for whole number solutions for b and c. To find one, we can try various values of b and check if the resulting c is an integer.
Let's start by trying \(b = 15\):
\[196 + 15^2 = c^2\]
\[196 + 225 = c^2\]
\[421 = c^2\]
However, \(c^2 = 421\) doesn't yield a whole number value for c.
Let's try \(b = 16\):
\[196 + 16^2 = c^2\]
\[196 + 256 = c^2\]
\[452 = c^2\]
Similarly, \(c^2 = 452\) doesn't give us a whole number value for c.
It seems that \(b = 14\) (which would make \(a = b\)) would give a Pythagorean triplet:
\[14^2 + 14^2 = c^2\]
\[196 + 196 = c^2\]
\[392 = c^2\]
Therefore, the Pythagorean triplet with one member as 14 is (14, 14, 392).
