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

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

Grade:11

2 Answers

Devendra pratap singh
14 Points
6 years ago
2^8+2^11+2^n is relate with a^2+2ab+b^2So here (2^4)^2+2×2^4×2^6+(2^3)^2={(2)^4+(2)^3}^2So now we get2×2^4×2^n=2×2^4×2^6So here n=6
Arun
25750 Points
6 years ago
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
 
 
Regards
Arun (askIITians forum expert)

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