Question

PLZZZ SOLVE IT . ....

Let P (n) stand for the statement : "3^(2n+2) - 8n –9 is divisible by 64”.
Show that if P(m) is true, then P (m+1) is also true, m€N​

Answer 1

Answer:

For P(m) = 3^( 2 m + 2) - 8m - 9 = 64 d

3^( 2 m + 2) - 8m = 64d + 9 + 8m --> ( i)

Now, P( m + 1) = 3^( 2.{m+1} +2) - 8( m +1) - 9

P ( m +1) = 3^( 2m + 4) - 8 ( m +1) - 9

=> 3^( 2m + 2). 3^2 - 8 ( m +1) - 9

=> 3^( 2m + 2). 9 - 8(m +1) - 9

From (i)

=> ( 64d + 9 + 8m). 9 - 8m - 8 - 9

=> 576 + 81 + 72m - 8m - 17

=> 64m + 640 = 64 ( m +10)

Let m + 10 = lambda

So, P ( m +1) = 64 lambda

P (m +1) is also true.

♥️QED