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प्रश्न
Write two Pythagorean triplets each having one of the numbers as 5.
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उत्तर
Given: We know that for any natural number greater than 1, (2m, m2 – 1, m2 + 1) is a the Pythagorean triplet.
So if one number is m2 + 1 then other two number are m2 – 1 and 2m.
i.e. m2 + 1 = 5 ...(Given)
⇒ m2 = 4
⇒ m = 2
Then m2 – 1
= 22 – 1
= 4 – 1
= 3
And 2m = 2(2) = 4
Hence, Pythagorean triplet is 3, 4 and 5
Similarly another triplet is:
- We need a2 + b2 = c2
- Let's try b = 12 and solve for c:
- 52 + 122 = 25 + 144 = 169
- c2 = 169
- c = `sqrt(169)` = 13
Thus, the triplet is (5, 12, 13).
Hence, 3, 4, 5 and 5, 12, 13 are two Pythagorean triplet.
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