Question

For a GP prove that am+n × am-n = am²​

Answer 1

Answer:

LHS = RHS.

Step-by-step explanation:

$a(m + n) \times a(m - n) =a {(r)}^{m + n - 1} \times a {(r)}^{m - n - 1} \\ \\ = {a}^{2} {(r)}^{(m - 1 + n) + (m - 1 - n)} \\ \\ = {a}^{2} {(r)}^{2(m - 1) } \\ \\ = { ({(ar)}^{m - 1}) }^{2} \\ \\ = ({a(m))}^{2} = rhs.$