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mukushla

  • 3 years ago

How many natural numbers \(n\) are there such that\[\sqrt{n+\sqrt{n+\sqrt{n+\sqrt{n+...}}}}\]is natuaral too.

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  1. hartnn
    • 3 years ago
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    p^2 - p - n =0

  2. mukushla
    • 3 years ago
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    n=2,6 gives 2 and 3 ,... ??? are there more numbers?

  3. sauravshakya
    • 3 years ago
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    |dw:1347788157019:dw| then, a^2=n+a

  4. sauravshakya
    • 3 years ago
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    Now, a and n has to be natural too

  5. jiteshmeghwal9
    • 3 years ago
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    but that's the value of the total equation @sauravshakya :(

  6. mukushla
    • 3 years ago
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    n is natuaral... a has to be natural :)

  7. sauravshakya
    • 3 years ago
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    Ya.......... thinking on it...... I think it will lead to solution

  8. sauravshakya
    • 3 years ago
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    n=a^2-a

  9. jiteshmeghwal9
    • 3 years ago
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    that's it because if we right the equation as\[\sqrt{n+\sqrt{n+\sqrt{n.....}}}=x\]then we find the value of 'x' to get the answer & u did the same.

  10. sauravshakya
    • 3 years ago
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    If a=2 then n=2, If a=3 then n=6...

  11. sauravshakya
    • 3 years ago
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    infinite solutions

  12. sauravshakya
    • 3 years ago
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    If a=4 then n=12, If a=5 then n=20 ...

  13. sauravshakya
    • 3 years ago
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    right? @mukushla

  14. mukushla
    • 3 years ago
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    right :)

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