Question

1. How to find out whether the 3 numbers which are given are Pythagorean Triplets or not ?

2. Tell whether 2,3 & 5 are Pythagorean Triplets or not ?

3. Also tell whether 6,8 & 10 Pythagorean Triplets or not ?


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Answer 1

Answer :

1. It's Easy to Find whether The 3 Numbers which are given to us are triplet or not !

➝In Pythagorean Triplets or we can say Pythagorean Theorem it's stated that The Square of the largest Number is equal to the Sum of the Squares of the Rest 2 Smaller Numbers !

➝ The formula for Pythagorean Triplets are :

• ➝ a2+b2 = c2

So , By simply putting the Numbers which are given to you in the formula can show that the numbers are Triplet or Not !

2. Let's solve it !

➝ Numbers given to us are : 2 , 3 & 5 .

Formula for Triplet is : a2 + b2 = c2

➝ 2^2 + 3^2 = 5^2

➝ 4 + 9 = 25

➝ 13 = 25

The Answer is NO !

3. Let's solve this too !

➝a2 + b2 = c2

➝ 6^2 + 8^2 = 10^2

➝ 36 + 64 = 100

➝100=100

The Answer is Yes !

Answer 2

Answer:

1. A Pythagorean triple is a list of three numbers that works in the Pythagorean theorem — the square of the largest number is equal to the sum of the squares of the two smaller numbers. The multiple of any Pythagorean triple (multiply each of the numbers in the triple by the same number) is also a Pythagorean triple.
2. $Pythagorean \: triple \: consists \: of \: three \\ \: positive \: integers a, \: b \: and \: c, \: such \\ \: that \: {a}^{2} \: {b}^{2} \: {c}^{2} . Such \: a \: triple \: is \\ \: commonly \: written \: (a, \: b, \: c), \: and \\ \: a \: well-known \: example \: is \: \\ (3, \: 4, \: 5). \: However, \: right \: triangles \\ \: with \: non-integer \: sides \: do \: not \\ \: form \: Pythagorean \: triples.$
3. Every integer greater than 2 is part of a primitive or non-primitive Pythagorean triple. For example, the integers 6, 10, 14, and 18 are not part of primitive triples, but are part of the non-primitive triples (6, 8, 10), (14, 48, 50) and (18, 80, 82).