我有１題數學5識...help me (10點)

2007-07-24 7:04 pm

第1題
Find a two-digit number that satisfies the following conditions :

(1)The tens-digit is greater that the unit-digit by 2.

(2)The square of the unit-digit is karger that twice the tena-digit.

A possible solution is 64 .Would you suggest other solutions?

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回答 (4)

格古洛

2007-07-24 8:36 pm

✔ 最佳答案

Let x be the tens-digit , y be the unit-digit
then , x-y=2------------(1)
and y ^2 > 2 x---------(2)

satisfies the above conditions

put (1) x=2+y into (2)
y^2>2(2+y)
=> y^2>4+2y
=> y^2-2y-4>0
=> y^2-2y+1-5 >0
=> (y-1)^2-5>0

so y >4(y<10), that mean
y=4, x=2+y=6
y=5, x=2+y=7
y=6, x=2+y=8
y=7, x=2+y=9
y=8, x=2+y=10(rejected)
y=9, x=2+y=11(rejected)

so the two-digit number will be 64, 75, 86, 97

參考: ME

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ho tong

2007-07-25 12:11 am

97 86 75 64

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鄒家敏

2007-07-24 8:31 pm

97
86
75
64

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