Question

Write a pythogorean triplet whose smallest member is 8

Answer 1

Answer:

pythogorean triplet of smallest member 8 is-

m=4, m=3

Answer 2

Solution:-

※ We can get Pythagorean triplets by using general form 2m, m² - 1, m² + 1.

★ Let us first take

$\large{\tt{\longmapsto{m^2 - 1 = 8}}}$

$\large{\tt{\longmapsto{m^2 = 8 + 1 = 9}}}$

$\large{\tt{\longmapsto{m = 3}}}$

$\large{\tt{\longmapsto{2m = 6}}}$

⠀⠀⠀⠀$\boxed{\sf{\orange{and}}}$

$\large{\tt{\longmapsto{m^2 + 1 = 10}}}$

⠀

※ The triplet is thus 6, 8, 10. But 8 is not the smallest member of this.

★ So, let us try

$\large{\tt{\longmapsto{2m = 8}}}$

$\large{\tt{\longmapsto{m = 4}}}$

$\large{\tt{\longmapsto{m^2 - 1 = 16 - 1 = 15}}}$

$\large{\tt{\longmapsto{m^2 + 1 = 16 + 1 = 17}}}$

⠀

★ The triplet is 8, 15, 17 with 8 as smallest member.

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