Question

write a Pythagorean triplet whose greatest number is 257

Answer 1

Answer:

32, 255, 257 is the pythagorean triplet requirded

Step-by-step explanation:

Answer 2

Answer:

The pythagorean triplet with the largest number as 257 is found to be: 32, 255, 257.

Step-by-step explanation:

We know, the pythagorean triplets are the three numbers which follow the pythagoras theorem which says:

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

where a, b, c are given by the following expressions:

$a=m^2-n^2\\b=2mn\\c=m^2+n^2$

Now, we know that in the pythagoras theorem, c is the largest number and here we are given the largest number as: 257

Representing 257 as the general form of c, we get:

$257=256+1$

$257=16^2+1^2$

So, comparing this result with the general form, we get:

m = 16 and n = 1,

Using the value of m and n to find a and b, we get:

For a: $a=m^2-n^2$, putting $m=16$ and $n=1$

$a=16^2-1^2$

$a=256-1$

or we can say:

$a=255$

For c: $c=2mn$, putting $m=16$ and $n=1$

$c=2\times16\times1$

or we can say:

$c=32$

Thus, the required pythagorean triplet is found to be: 32, 255, 257.