1. More about Pythagorean triplets
We have seen one way of writing pythagorean triplets as 2m, m2 -1, + 1.
A pythagorean triplet a, b, c means a² + b2 = c2. If we use two natural numbers m and n(m>n), and
take a = m2 – n?, b = 2mn, c = m2 + n², then we can see that ca = a + b2.
Thus for different values of m and n with m>nwe can generate natural numbers a, b, c such that they
form Pythagorean triplets.
For example: Take, m=2, n=1.
Then, a=m2 – n? = 3, b = 2mn=4,c=m2 + n2 = 5, is a Pythagorean triplet. (Check it!)
For, m = 3, n = 2, we get, tas
a=5, b= 12,c= 13 which is again a Pythagorean triplet.
Take some more values for mand n and generate more such triplets.
Answers
Step-by-step explanation:
Property 10 For any natural number m greater than 1(2m, m² − 1, m² + 1) is a pythagorean triplet.
A triplet (m, n, p) of three natural numbers m, n and p is called a pythagorean triplets if m² + n² = p².
If a and b are natural numbers and a > b, then show that (a² +6²), (a²- 6²) (2ab) is a Pythagorean triplet. Find two Pythagorean triplets using any convenient values of a and b.
Solve the any one of following sub questions: If m and n are two distinct numbers then prove that 2 m² -n², 2mn and m² + n² is a pythagorean triplet.
There positive numbers a b c in this order are said to form a 2 pythagorean triplet if c² = a² + b² +6²
If m and n are two distinct numbers such that m >n, then prove that m² n²,2mn and m² + n² is a Pythagorean triplet.
Suppose m and n are any two numbers. If m² n², 2mn and 2 m² + n² are the three sides of a triangle, then show that it is a right angled triangle and hence write any two pairs of Pythagorean triplet.
You know that if in a right angled triangle ABCa²+ b2 = c² If, a triplet a, b, c of positive integers is called a Pythagorean triplet. Some groups of three numbers are given below. Tell which are the Pythagorean triplets in them-
please mark me as the brainliest answer.
Answer:
10,8,6
3^2+1^2,3^2-1^2,2(3+1)