有一个两位数,它的十位数上数字与个位上数字之和是8,如果把十位上数字和个位上的数字调换后，所得两位数
设原来的两位数为10x y。 x y=8 (10y x)(10x y)=1855 100xy 10y^2 10x^2 xy=1855 101xy 10y^2 10x^2=1855 101x(8-x) 10(8-x)^2 10x^2=1855 808x-101x^2 10(64 x^2-16x) 10x^2=1855 808x-91x^2 640 10x^2-160x=1855 -81x^2 648x-1215=0 81x^2-648x 1215=0 Δ=419904-393660=26244 x=(648±2√6561)/162 =324/81±√6561/81 =4±3√729/81...全部
设原来的两位数为10x y。
x y=8 (10y x)(10x y)=1855 100xy 10y^2 10x^2 xy=1855 101xy 10y^2 10x^2=1855 101x(8-x) 10(8-x)^2 10x^2=1855 808x-101x^2 10(64 x^2-16x) 10x^2=1855 808x-91x^2 640 10x^2-160x=1855 -81x^2 648x-1215=0 81x^2-648x 1215=0 Δ=419904-393660=26244 x=(648±2√6561)/162 =324/81±√6561/81 =4±3√729/81 =4±√729/27 =4±3√81/27 =4±√81/9 =4±1 x=5或x=3 53、35 原来的两位数为53或35。收起
