Question

For any natural number m greater than 1, which of the following triplets
is Pythagorean?
(a) (2m, 2m² - 1,2m² + 1)
(b) (m, m- 2, m² + 2)
(c) (2m, m - 1, m² + 2)
(d) (m‹2 - 1,2m, m’ + 1)​

Answer 1

Answer:

Step-by-step explanation:

Let a=m  

2

−1

b=2m

c=m  

2

+1

using pythagoras theorem, a  

2

+b  

2

=c  

2

 

So, (m  

2

−1)  

2

+4m  

2

=(m  

2

+1)  

2

 

m  

4

+1−2m  

2

+4m  

2

=(m  

2

+1)  

2

 

m  

4

+2m  

2

+1=(m  

2

+1)  

2

 

(m  

2

+1)  

2

=(m  

2

+1)  

2

 

Since LHS=RHS , we can say that a,b,c always form pythagorean triplet.

Answer 2

Step-by-step explanation:

A triplet for any natural number m is greater than 1 (2m, m^2-1,m^2+2) is a pythagorean triplet. option c is not a correct because no monomial not reacted a square.