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

Devendra pratap singh
14 Points
```							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
```
2 years ago
Arun
23331 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 = 2^4n-8 = 4n = 12  RegardsArun (askIITians forum expert)
```
2 years ago
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### Course Features

• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions