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Köklü İşlem

Bu soru 26 Temmuz 2009 tarihinde ZekiAdam tarafından gönderildi

Bildiğimiz gibi (1+√2 )= 2,41421356… diye devam eden irrasyonel bir sayıdır. Bu sayının 2009. kuvvetini aldığımızda oluşacak sayının ondalık yazılımında kesir virgülünden sonra gelen 209. sayı nedir?

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1 vote, average: 1,00 out of 51 vote, average: 1,00 out of 51 vote, average: 1,00 out of 51 vote, average: 1,00 out of 51 vote, average: 1,00 out of 5 (1 Üye oyladı, Ortalama puan: 1,00)
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“Köklü İşlem” için 7 Yorum

  1. semihcokceken dedi ki:

    (1+kök2)^n=a+bkök2 ise (1-kök2)^n=a-bkök2 dir.taraf tarafa toplarsak (1+kök2)^2009+(1-kök2)^2009=2a olur ki bu da virgülden sonra hep sıfır olduğunu gösterir.2a,00000000000000… gibişimdi (1+kök2)^2009 = 2a + (kök2-1)^2009 olur kikök2-1 ifadesi 1/2 den küçüktür 10.kuvvetini alırsak(kök2-1)^10<1/1024<10^-3=0.001 olur ki(kök2-1)^2009<<(kök2-1)^2000<10^-600=0.000…0001(599 tane sıfır)elde edilir.(1+kök2)^2009 = 2a + (kök2-1)^2009 doğal olarak virgülden 599 tane sonrası sıfır olur.

    • yuckfou dedi ki:

      Sanki ufak bikaç eksiklik bırakmışsın gibime geldi örneğin senin mantığına göre sayımızın 2008. kuvvetinin 208. basamığını soruyo olsaydık gene 0 bulacakmışız gibi bi anlam çıkardım ama orada 208. hane 9 olur.

      neyse aşağıdaki yorumdaki çözümün daha komple olduğunu düşünmekle birlikte değerlendirme yapıyo olsaydık senin de bu çözümle en az 99/100 alabilceğini düşünüyorum.

  2. kurutmaz dedi ki:

    (1-?2))^2009+(1+?2)^2009=a olsun
    a elamanıdır z(tam sayılar kümesi)
    demek ki (1-?2))^2009 sayısının ondalık yazılımındaki virgülden sonrası ile (1+?2)^2009 virgülden sonrası aynı olmalıdır.
    (çünkü (1-?2))^2009 sayısı negatiftir)
    (1-?2)^2009 sayısı yaklaşık olarak -0,42 ye eşittir.
    (-0,42)^2009 ise aşırı küçük bir sayıdır ve 209. basamağı 0 olmak zorundadır.
    buna göre (1+?2)^2009 sayısının da 209. basamağı 0 dır

  3. sahin dedi ki:

    Tebrikler kurutmaz… cevap gayet carpici… kutluyorum…

  4. asliersin dedi ki:

    Sonuç bikere 2 den büyük olmak zorunda 2^n her zaman büyük veya eşit 2 dir. n=0 veya küçük 0 olmadı sürece eee ozaman 2 nn 2009 unca kuvveti 0…. bişi olamaz yukarıdaki cvp ları anlamdım kısacası

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    sonuç bu 209.cusunuda siz buluverin artıkm:d

    • MyNameis_HIDIR dedi ki:

      Bi yanlış anlaşma olmuş sanırım

      soruda sayının herhangi bir sayıdan küçüklüğü ya da büyüklüğü sorulmuyor sadece virgülden sonraki 209. basamağındaki sayı soruluyor.

      örneğin 2,5^3 sayısı

      15,625 tir ve yine 2 den 3ten ya da 5 ten büyük bir sayı olmasına rağmen virgülden sonraki 2. sayı nedir dersek buna yoktur ya da belirlenemez diyemeyiz. görüldüğü üzere virgülden sonraki 2. sayı 2 dir.
      —–
      yukarda yazdığın bilmemkaç basamaklı sayıya gelirsek bir irrasyonel sayının bu şekilde sonlu sayıda rakam kullanarak ondalık yazılımını yapamazsın, yukardaki çözümlerde de göreceğin üzere buna gerek de yok. sadece virgülden sonraki kısımları bizi ilgilendiriyor, ki eşleniği olan ve -1 ile 1 arasına düşen sayının kuvvetini alıp 0 a çok yakın bir sayı olduğunu bulmak yoluyla bunu arkadaşlarımız çözdüler.

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