ที่หลุมฝังศพของ Diophantus นักคณิตศาสตร์ผู้มีชีวิตอยู่ระหว่างประมาณปี ค.ศ. 246 - ค.ศ. 330
ได้มีคำจารึกไว้ว่า "Diophantus ใช้ชีวิตในวัยเด็กเท่ากับ 1/6 ของชีวิตของเขา
ในวัยหนุ่มเท่ากับ 1/12 ของชีวิตของเขา และหลังจากนั้นอีก 1/7 ของชีวิตเขาอยู่เป็นโสด
ภรรยาเขาคลอดลูกหลังจากแต่งงานแล้ว 5 ปี ลูกของเขาตายก่อนเขา 4 ปี
ในขณะที่มีชีวิตเท่ากับครึ่งหนึ่งของชีวิตเขา"
ถามว่า Diophantus เสียชีวิตเมื่ออายุเท่าไร

เฉลย >> โจทย์ข้อนี้ต้องตั้งสมการอย่างเดียวครับ
ก่อนอื่นเราต้องสมมติให้ Diophantus มีอายุ x ปี (ตั้งแต่เกิดจนเสียชีวิต)
ชีวิตในวัยเด็ก x ÷ 6 ปี
ชีวิตในวัยหนุ่ม x ÷ 12 ปี
อยู่เป็นโสด x ÷ 7 ปี
แต่งงานและมีลูก 5 ปี
-------------------------------------------->>ลูกเกิด
ลูกของเขาตายก่อนเขา 4 ปีในขณะที่มีชีวิตเท่ากับครึ่งหนึ่งของชีวิตเขา
หมายความว่า อายุลูกก่อนตาย คือ x ÷ 2 ปี
และเมื่อลูกตายเขาอยู่ต่อไปได้อีก 4 ปี

ตั้งสมการได้ดังนี้ (x ÷ 6) + (x ÷ 12) + (x ÷ 7) + 5 + (x ÷ 2) + 4 = x
เมื่อแก้สมการจะได้ x = 84 เป็นคำตอบครับ

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ยอน

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ช่วยบอกขั้นตอนการแก้สมการข้อนี้หน่อยได้มั้ยคะ

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mathkungs

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ครน ของ 6 12 7 2 คือ 84 ครับ
เพราะฉะนั้นเราต้องทำ ส่วน(เศษส่วน) ให้มีค่าเท่ากับ 84 ให้หมดทุกพจน์ก่อนจะได้ว่า
(14x / 84) + (7x / 84) + (12x / 84) + (420 / 84) + (42x / 84) + (336 / 84) = x
(14x + 7x + 12x +420 +42x +336) / 84 = x
14x + 7x + 12x +420 +42x +336 = 84x
75x + 756 = 84x
756 = 9x
x = 84
ขอโทษครับที่มาตอบช้า

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- -
จะถามไมเยอะแยะ

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