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چهار سوی علوم - مسائل ریاضی4
جمعه 13 اسفند 1389  01:39 ب.ظ
توسط: حسام

سلام خدمت تمامی ریاضی دوستان

نمی دونم سئوالات من آسون بود و شما به خاطر اسون بودنش جواب ندادین. یا چی بگم به هر حال حل جوابها در قسمت پائین آورده شده امیدوارم که بتونم کمکی کرده باشم.

با تشکر مدیر وبلاگ

 

۱- حاصل ضرب این ضرب را می توان اینطور نوشت:

 

BBB = B × 111 = B ×3 ×37

 

چون 37 عددی اول است بنابراین یکی از دو عامل ضرب (AB یا CD) می تواند 37 یا 74 باشد در اینصورت عامل دیگر به ترتیب برابر B ×3 یا (B × 3 ) ÷ 2 خواهد شد. در حالت دوم B باید رقمی زوج باشد. و چون داریم      (B × 3 ) ÷ 2 > 10

 بنابراین تنها B = 8 ممکن است. ولی جوابی که از این راه بدست می آید: 74  × 12 = 888 با یکی از شرط های مسئله نمی سازد (باید هر رقم حاصل ضرب برابر رقم یکان یکی از دو عامل ضرب باشد) در نتیجه یکی از دو عامل ضرب تنها 37 می تواند باشد اگر عامل اول ضرب را 37 بگیریم حاصل ضرب باید 777 شود که در این صورت عامل دوم ضرب برابر 21 می شود. ولی اگر عامل دوم ضرب را 37 فرض کنیم باید داشته باشیم

 

10 A + B = 3B Þ 5A = B

 

که از آنجا A = 1 و B = 5 بدست می آید. به این ترتیب برای مساله دو جواب پیدا می شود:

 

37 × 21 = 777

15 × 37 = 555

 

2- فرض می کنیم که (n+1) امین جمله تصاعد اول با (m+1) امین جمله تصاعد دوم برابر باشد. (n+1) امین جمله تصاعد اول برابر است با 2 + 5n و (m+1) امین جمله تصاعد دوم برابر است با 2 + 3m و بنابراین فرض باید داشته باشیم:

2 + 5n = 2 + 3m Þ n = 3m/5

 

اگر m برابر با 5  , 10 , 15 و غیره باشد  برای n به ترتیب عددهای 3 , 6 , 9 و ... بدست می آید. از آنجا می بینیم که جمله های برابر عبارتند از هر سه جمله یکبار در تصاعد اول و هر پنج جمله یکبار در تصاعد دوم. بنابراین تعداد جمله های مساوی در 60 جمله تصاعدها برابر است با 60 ÷ 5 = 12  

 

3-  دو راه حل برای این مساله داریم . شما هم می توانید راه حل های دیگری پیدا کنید:

 

(2 × 2 × 2) – (2 ÷ 2) = 7

(22 ÷ 2) – 22  = 7

 

4- از راه حل های ممکن چند تا را در اینجا آورده ایم:

97524 ÷ 10836 = 9

95823 ÷ 10647 = 9

95742 ÷ 10638 = 9

0 × 12345678 + 9 = 9

123456790  + 8 = 9


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