is (3,4,5) are Pythagorean triplets by 2m formula
Answers
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The three whole number side-lengths are called a Pythagorean triple or triad. An example is a = 3, b = 4 and h = 5, called "the 3-4-5 triangle". We can check it as follows: 32+42 = 9 + 16 = 25 = 52 so a2 + b2 = h2.
Answer:
The 2 m formula states :
( 2 m )² + ( m² - 1 )² = ( m² + 1 )²
Put m = 2
⇒ ( 2 × 2 )² + ( 2² - 1 )² = ( 2² + 1 )²
⇒ 4² + ( 4 - 1 )² = ( 4 + 1 )²
⇒ 16 + 3² = 5²
⇒ 16 + 9 = 25
⇒ 25 = 25
Hence m × 2 = 2 × 2 = 4
m² - 1 = 3
m² + 1 = 5
They are Pythagoran triplets .
Hence proved !
Step-by-step explanation:
What is 2 m formula ?
Let the numbers which form a Pythagorean triplet be a , b , c
a , b , c are Pythagoran triplets .
∵ Substitute the values with ( 2 m ) + ( m² - 1 ) = ( m² + 1 )
This is the formula for checking triplets .
It was invented by Plato , a Greek mathematician .
The above formula has a proof ( I forgot it :D )