f4 maths

設該整數 = 10a + b ,
十位數字與個位數字對調後 = 10b + a , 其數值會減少45
得
10a + b = 10b + a + 45......(1)
a^2 + b^2 = 73......(2)
由(1) :
9a - 9b = 45
a - b = 5
a = b + 5 , 代入(2) :
(b+5)^2 + b^2 = 73
b^2 + 10b + 25 + b^2 = 73
2b^2 + 10b - 48 = 0
b^2 + 5b - 24 = 0
(b - 3)(b + 8) = 0
b = 3 或 b = - 8 (捨去)
a = b+5 = 3+5 = 8
答案是 10a + b = 80 + 3 = 83