Question

2 power m+ 1 added to 2 power m-1 which is equal to 640

Answer 1

m = 8   if   $2^{(m+1)} + 2^{(m-1)} = 640$

Step-by-step explanation:

$2^{(m+1)} + 2^{(m-1)} = 640$

$2^{(m-1 + 2)} + 2^{(m-1)} = 640\\2^2 *2^{(m-1)} + 2^{(m-1)} = 640\\4 *2^{(m-1)} + 2^{(m-1)} = 640\\2^{(m-1)} (4 + 1) = 640\\2^{(m-1)} (5) = 640\\2^{(m-1)} = 128\\2^{(m-1)} = 2^7$

Equating Powers

m -1  = 7

=> m = 8

Verification :

2⁹ + 2⁷  = 512 + 128  = 640

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