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Let y be the life of Diophantus

y/6 + y/12 + y/7 + 5 + y/2 + 4 = y
9 = y - y/6 - y/12 -y/7 - y/2
9 = y (1 - 1/6 - 1/12 -1/7 - 1/2)
9 = y [1(7)(12) - 1(2)(7) - 1(7) - 1(12) - 1(6)(7)] / [(12)(7)]
9(12)(7) = y (84-14-7-12-42)
y = 756 / 9
y = 84

Therefore, the life of Diophantus is 84 year.

2009-01-03 09:03:47 補充：
1/6 of his life was a happy childhood. = 其中1/6生命係快樂童年
After another 1/12 of his life, he grew a bread. = 生命另外1/12 (grew a bread唔係好知中文係咩)
Then he was married. For 1/7 of his life after marriage, he did not have a child. = 之後生命的1/7結婚,但未有仔女

2009-01-03 09:03:55 補充：
5 more years later, his son was born. = 5年後有個仔
Unluckily his son died at 1/2 of his father's age. = 係他生命的一半,不幸地他仔死左
He then lives in sorrow for only 4 more years before he passed away. = 他4年後就死

Let x be the life of Diophantus

x/6 + x/12 + x/7 + 5 + x/2 + 4 = x
14x+ 7x+ 12x+ 420+ 42x+ 336=84x(全部乘84)
75x+756=84x
9x=756
x=84
Therefore, he had lived for 84 years.