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Eğitmen, Harvard-MIT arasında düzenlenen matematik turnuvasından bir soruyu çözmektedir.","Videoda, 2018 yılında düzenlenen Harvard-MIT matematik turnuvasından seçilen bir sayı sorusu çözülmektedir. Eğitmen, soruyu adım adım çözerken, köklerin çarpımı, tam sayı olma koşulları ve sayı teorisi gibi matematiksel kavramları kullanmaktadır. Soru, en küçük pozitif tam sayı n'yi bulmayı gerektirmekte ve çözüm sürecinde k'nin çift olması ve 20'nin karesinden küçük olması gibi önemli noktalar vurgulanmaktadır. Eğitmen, bu serinin devam edeceğini ve gelecekte integral yarışmaları gibi daha zor sorular çözeceğini belirtmektedir."]},"endTime":550,"title":"Harvard-MIT Matematik Turnuvası Soru Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"Harvard-MIT Matematik Turnuvası","list":{"type":"unordered","items":["Konuşmacı, Harvard-MIT arasında yapılan matematik turnuvasından bir soru çözeceğini belirtiyor.","Turnuvada öğrenciler daha hızlı çözmeye çalışıyor ve integral yarışmaları düzenleniyor.","Konuşmacı, bu turnuvadan beş soruyu çözeceğini ve ilgi gösterilirse devamı geleceğini söylüyor."]},"beginTime":0,"endTime":84,"href":"/video/preview/6487538118996561816?parent-reqid=1774371879958070-857570504229888320-balancer-l7leveler-kubr-yp-vla-184-BAL&text=Mathematician+Records&t=0&ask_summarization=1"},{"index":1,"title":"Sorunun Tanıtımı","list":{"type":"unordered","items":["Soru, komple pozitif integer n için √(100+√n) - √(100-√n) ifadesinin tam sayı olması için en küçük n değerini bulmayı gerektiriyor.","Konuşmacı, sorunun zor olmadığını ve diğer soruların nispeten daha zor olduğunu belirtiyor."]},"beginTime":84,"endTime":144,"href":"/video/preview/6487538118996561816?parent-reqid=1774371879958070-857570504229888320-balancer-l7leveler-kubr-yp-vla-184-BAL&text=Mathematician+Records&t=84&ask_summarization=1"},{"index":2,"title":"Sorunun Çözümü","list":{"type":"unordered","items":["Konuşmacı, ifadeyi k olarak tanımlayarak karesini alıyor ve 100+√n - √(100-√n) = k² şeklinde yazıyor.","İşlem sonucunda 200+2√(100+√n)(100-√n) = k² denklemi elde ediliyor.","√(100+√n)(100-√n) ifadesinin çift sayı olması gerektiği ve k'nın çift sayı olması gerektiği çıkarılıyor."]},"beginTime":144,"endTime":378,"href":"/video/preview/6487538118996561816?parent-reqid=1774371879958070-857570504229888320-balancer-l7leveler-kubr-yp-vla-184-BAL&text=Mathematician+Records&t=144&ask_summarization=1"},{"index":3,"title":"Sonuç","list":{"type":"unordered","items":["k'nın çift sayı olması ve 20+2√(100+√n)(100-√n) ifadesinin 20'nin karesinden küçük olması gerekiyor.","k=18 alındığında, 20+2√(100+√18)(100-√18) = 324 denklemi elde ediliyor.","324 = 20+2√(100+√18)(100-√18) denkleminden n=6156 olarak bulunuyor."]},"beginTime":378,"endTime":533,"href":"/video/preview/6487538118996561816?parent-reqid=1774371879958070-857570504229888320-balancer-l7leveler-kubr-yp-vla-184-BAL&text=Mathematician+Records&t=378&ask_summarization=1"}],"linkTemplate":"/video/preview/6487538118996561816?parent-reqid=1774371879958070-857570504229888320-balancer-l7leveler-kubr-yp-vla-184-BAL&text=Mathematician+Records&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Harvard-MIT Matematik Turnuvası Sorusu! 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