Question

Write a Pythagorean triplet whose smallest number is 8​

Answer 1

(8,15,17)

Explanation:

Lets verify

`\\ \sf\longmapsto 8^2+15^2=17^2`

`\\ \sf\longmapsto 64+225=289`

`\\ \sf\longmapsto 289=289`

Hence verified

Answer 2

• 8, 15, 17

Explanation:

Pythagorean triplets are a, b and c with property of:

• a² + b² = c², where a, b, c are different positive integers

Let a = 8, find b and c.

The we have:

• 8² + b² = c²
• c² - b² = 64
• (c + b)(c - b) = 64

Options:

64 = 64*1 = 32*2 = 16*4 = 8*8

1)

• c + b = 64
• c - b = 1

Add up to get:

• 2c = 65 ⇒ c = 32.5 - is not an integer, no solution

2)

• c + b = 32
• c - b = 2

Add up to get:

• 2c = 34
• c = 17 ⇒ b = 15

The triplet is 8, 15, 17

3)

• c + b = 16
• c - b = 4

Add up to get:

• 2c = 20
• c = 10 ⇒ b = 6 < 8, b is smaller than 8, no solution

4)

• c + b = 8
• c - b = 8

Add up to get:

• 2c = 16
• c = 8 ⇒ b = 0, no triplet, no solution