Question #21783

Suppose that {a, b, c}is a pythagorean triple. Give some examples that will show that {3a+4b, 4a-3b, 5c} is pythagorean triple.

Expert's answer

If {a, b, c}is a pythagoreantriple then:

a^2+b^2=c^2

And for {3a+4b, 4a-3b, 5c}:

(3a+4b)^2 + (4a-3b)^2 = (5c)^2

9a^2 + 12ab + 16b^2 + 16a^2 - 12ab + 9b^2 =25c^2

25a^2 + 25b^2 = 25c^2

a^2+b^2=c^2

It means that if {a, b, c}is a pythagorean triplethen {3a+4b, 4a-3b, 5c} is pythagorean triple too.

a^2+b^2=c^2

And for {3a+4b, 4a-3b, 5c}:

(3a+4b)^2 + (4a-3b)^2 = (5c)^2

9a^2 + 12ab + 16b^2 + 16a^2 - 12ab + 9b^2 =25c^2

25a^2 + 25b^2 = 25c^2

a^2+b^2=c^2

It means that if {a, b, c}is a pythagorean triplethen {3a+4b, 4a-3b, 5c} is pythagorean triple too.

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