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Grade: 11
Find the no of values of n for which 2^8 + 2^11 + 2^n is a perfect square
2 years ago

## Answers : (1)

Arun
23330 Points

Dear student

2^8 + 2^11 + 2^n
= 2^8 ( 1 + 2^3 + 2^(n-8) )
= 2^8 (9 + 2^(n-8) )

Now for this to be a perfect square,

9 + 2^(n-8) sbould be a perfect square.

Hence 9 + 16 = 25 is a perfect square.

2^(n-8) = 16 = 2^4
n-8 = 4
n = 12
2 years ago
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