Find a Pythagoras triplet whose one member (i) 15 (ii) 25 (iii) 10 (iv

1.	Find a Pythagoras triplet whose one member (i) 15 (ii) 25 (iii) 10 (iv) 5.
Answer» (2m, m² - 1 , m² + 1) is a pythagorean triplet (i) Let m² - 1 = 15 ⇒ m² = 16 = 42 ⇒ m = 4 ∴ 2m = 2 x 4 = 8 m² + 1 = 16 + 1 = 17 ∴ (8, 15, 17) is a pythagorean triplet. (ii) Let m² + 1 = 25 ⇒ m² = 24 = 4 x 6 ∴ m = 2√6 ∴ 2m = 4√6 & m² - 1 = 24 - 1 ∴ (4√6, 23, 25) is a pythgorean triplet. (iii) Let 2m = 10 ⇒ m² - 1 = 25 - 1 = 24 m² + 1 = 25 + 1 = 26 ∴ (10, 24, 26) is a pythagorean triplet. (iv) Let m² + 1 = 5 ⇒ m² = 5 - 1 = 4 = 2² ∴ m = 2 ∴ 2m = 4 m² - 1 = 4 - 1 = 3 Hence, (4, 3, 5) is a pythagorean triplet.

Find a Pythagoras triplet whose one member (i) 15 (ii) 25 (iii) 10 (iv) 5.

Answer»

(2m, m² - 1 , m² + 1) is a pythagorean triplet

(i) Let m² - 1 = 15

⇒ m² = 16 = 42

⇒ m = 4

∴ 2m = 2 x 4 = 8

m² + 1 = 16 + 1 = 17

∴ (8, 15, 17) is a pythagorean triplet.

(ii) Let m² + 1 = 25

⇒ m² = 24 = 4 x 6

∴ m = 2√6

∴ 2m = 4√6

& m² - 1 = 24 - 1

∴ (4√6, 23, 25) is a pythgorean triplet.

(iii) Let 2m = 10

⇒ m² - 1 = 25 - 1 = 24

m² + 1 = 25 + 1 = 26

∴ (10, 24, 26) is a pythagorean triplet.

(iv) Let m² + 1 = 5

⇒ m² = 5 - 1 = 4 = 2²

∴ m = 2

∴ 2m = 4

m² - 1 = 4 - 1 = 3

Hence, (4, 3, 5) is a pythagorean triplet.

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