Question

Prove directly:
Given that a, b, c is a Pythagorean triple, prove that qa, qb, and qc is a Pythagorean triple where q is contained in R, q does not equal 0.

Answer 1

\[
(qb)^2 + (qc)^2 = q^2 b^2 + q^2 c^2= q^2(b^2+c^2)
\]
Can you finish it now?

Answer 2

Notice that
\[
b^2 + c^2 = a^2
\]

Answer 3

\[
(qb)^2 + (qc)^2 = q^2 b^2 + q^2 c^2= q^2(b^2+c^2)= q^2 a^2

\]

Answer 4

\[
q^2 a^2 = (qa)^2
\]

Answer 5

Can you explain in more detail from the first step.

Answer 6

Do you know that
\[

(x y)^2= x^2 y^2 \]?

Answer 7

Do you know that \( mn + m p = m(n+p) \)?

Answer 8

yes I do

Answer 9

In this case, you should understand step 1

Answer 10

yes

Answer 11

Do you understand the whole process now?

Answer 12

Can you write it step by step. Im losing the beginning.