Question

What is the Pythagorean triplet, whose one member is $34$?

• A. $34,278,290$
• B. $34,288,291$
• C. $34,288,290$
• D. $35,288,290$

Answer 1

The correct option is C $34,288,290$

For any natural numbers m > 1, $2m,m^2-1$, $m^2+1$ forms a Pythagorean triplet.
If we take $m^2+1=34$, then $m^2=33$
The value of m will not be an integer.
If we take $m^2-1=34$, then $m^2=35$
Again the value of m will not be an integer.
Let $2m=34$
$m=\frac{34}{2}$
$m=17$
$2m=2\times 17=34$
$m^2-1$ = ${17}^2-1$
$=289-1=288$
$m^2+1$ = ${17}^2+1$
$=289+1=290$
Therefore, the Pythagorean triplets are $34,288,290.$