Question

If a and b are any two natural numbers and a2 - b2, 2ab and a² + b2 are the three
sides of a tringle. Show that it is a right angled triangle and hence write any one
Pythagorean triplet.
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Answer 1

Answer:

Abhi abhi to mile the

Phir juda ho gaye

Kya thi meri khata

Tum sazah ho gaye

Mujhe khone ke baad ik din

Tum mujhe yaad karoge,

Phir dekhna milne ki mujhse

Tum fariyad karoge.

Answer 2

Step-by-step explanation:

Given If a and b are any two natural numbers and a2 - b2, 2ab and a² + b2 are the three sides of a tringle. Show that it is a right angled triangle and hence write any one Pythagorean triplet.

• So we have a right angled triangle A,B and C, in which BC is base and AC is the hypotenuse.
• Now we have (a – b)^2 = a^2 + b^2 – 2ab
•       (a^2 – b^2)^2 = a^4 + b^2 – 2 a^2b^2
• Also (2ab)^2 = 4a^2b^2
• Also (a^2 + b^2)^2 = a^4 + b^4 + 2a^2b^2
• So in a right angled triangle by Pythagoras theorem
•         AC^2 = AB^2 + BC^2
•               (a^2 + b^2)^2 = (a^2 – b^2)^2 + (2ab)^2
•      a^4 + b^4 + 2a^2b^2 = a^4 + b^2 – 2 a^2b^2 + 4 a^2 b^2
•     a^4 + b^4 + 2a^2b^2 = a^4 + b^4 + 2a^2b^2  
•  So both are equivalent and hence ABC is a right angled triangle.
• Now any one Pythagorean triplet will be 5, 12 and 13.
•           Since 13^2 = 5^2 + 12^2

Reference link will be

https://brainly.in/question/14561245