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mukushla Group Title

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

  • one year ago
  • one year ago

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  1. hartnn Group Title
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    p^2 - p - n =0

    • one year ago
  2. mukushla Group Title
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    n=2,6 gives 2 and 3 ,... ??? are there more numbers?

    • one year ago
  3. sauravshakya Group Title
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    |dw:1347788157019:dw| then, a^2=n+a

    • one year ago
  4. sauravshakya Group Title
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    Now, a and n has to be natural too

    • one year ago
  5. jiteshmeghwal9 Group Title
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    but that's the value of the total equation @sauravshakya :(

    • one year ago
  6. mukushla Group Title
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    n is natuaral... a has to be natural :)

    • one year ago
  7. sauravshakya Group Title
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    Ya.......... thinking on it...... I think it will lead to solution

    • one year ago
  8. sauravshakya Group Title
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    n=a^2-a

    • one year ago
  9. jiteshmeghwal9 Group Title
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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.

    • one year ago
  10. sauravshakya Group Title
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    If a=2 then n=2, If a=3 then n=6...

    • one year ago
  11. sauravshakya Group Title
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    infinite solutions

    • one year ago
  12. sauravshakya Group Title
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    If a=4 then n=12, If a=5 then n=20 ...

    • one year ago
  13. sauravshakya Group Title
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    right? @mukushla

    • one year ago
  14. mukushla Group Title
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    right :)

    • one year ago
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