幫下我做兩題數學題！

Let the original number be 10a + b
Thus, the reversed number will be 10b + a
Hence, [(10b + a) - (10a + b)] = 18
10b + a - 10a - b = 18
9b - 9a = 18
b = a + 2……….(i)
Given (10a + b)(10b + a) = 1855……….(ii)
Substitute (i) into (ii)
[10 a + (a + 2) ] [10(a + 2) + a] = 1855
[11a + 2] [11a + 20] = 1855
121a^2 + 22a + 220a + 40 - 1855 = 0
121a^2 + 242a - 1815 = 0
11a^2 + 22a - 165 = 0
(a - 3)(11a + 55) = 0
a = 3 or a = - 11 (rejected)
a = 3 is true
From (i)., b = a + 2 = 5
Ans. The original number is 35.

Let the age of the younger brother be a years
Let the age of the elder brother be b years
b = 2a
After 4 years, age of younger brother = a + 4
Age of elder brother = b + 4
(a + 4)^2 + (b + 4)^2 = 277……….(i)
Substitute b = 2a into (i)
(a + 4)^2 + (2a + 4)^2 = 277
a^2 + 8a + 16 + 4a^2 + 16a + 16 - 277 = 0
5a^2 + 20a - 245 = 0
a^2 + 4a - 45 = 0
(a - 5) (a + 9) = 0
a = 5 or a = -9 (rejected)
a = 5 is true
b = 2a = 2 * 5 = 10
Ans. The ages of the elder brother and younger brother are 10 years old and 5 years old respectively.
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