Question

Find the Pythagorean triplets, whose one member is $22.$

• A. $22,183,185$
• B. $22,483,485$
• C. $22,23,25$
• D. $22,120,122$

Answer 1

The correct option is D $22,120,122$

For any natural numbers m > 1, $2m,m^2-1$, $m^2+1$ form a Pythagorean triplet.
If we take $m^2+1=22$, then $m^2=21$
The value of m will not be an integer.
If we take $m^2-1=22$, then $m^2=23$
Again the value of m will not be an integer.
Let $2m=22$
$m=\frac{22}{2}$
$m=11$
$2m=2\times 11=22$
$m^2-1$ = ${11}^2-1$
$=121-1=120$
$m^2+1$ = ${11}^2+1$
$=121+1=122$
Therefore, the Pythagorean triplets are $22,120,122.$