Question

find the pythagorean triplet whose smallest number is 3 pls answer its urgent

Answer 1

Hey there !

Solution:

Let the members of the triplet be denoted as x² - 1, x², x² + 1.

Let the smallest number be denoted as x² - 1

So x² - 1 = 3

=> x² = 3 + 1 = 4

So second term is 4.

Third term is x² + 1 = 4 + 1 = 5

Hence the third term is 5.

Hence we get the triplet to be ( 3,4,5 )

This is also known as the golden triplet and is the first triplet in the number sequence which has all the numbers to be positive integers.

So let us verify it to be a triplet.

Pythagoras Theorem : a² + b² = c²

In this case let us assume a = 3 and b = 4. Now let us see whether we get c = 5. So substituting in the equation we get,

=> 3² + 4² = c²

=> 9 + 16 = c²

=> 25 = c²

=> c  = √ 25

=> c = +5 or -5

But side of a right angled triangle cannot be in negative. Hence the answer is +5.

Hence we get c = 5.

So the triplet with smallest number 3 is ( 3,4,5 ).

Hope my answer helped !

Answer 2

We know that for any natural number n > 1, then (2n, n^2 - 1, n^2 + 1) is Pythagorean  triplet.

Let n^2 - 1 = 3

= > n^2 = 1 + 3

= > n^2 = 4

= > n = 2 .

Then,

= > 2n = 4

= > n^2 - 1 = 3

= > n^2 + 1 = 5.

Therefore, the required pythagoroan triplet = (3,4,5).

Hope this helps!