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If m+n=11, m^2+n^2=99, what is m^3+n^3?A 3-digit number is subtracted from a 4-digit number and the result is a 3-digit number. The 10 digits are all different. What is the smallest possible result?xxxx-xxx=xxx PLEASE GIVE ME YOUR STEP!!!!!! 更新: 可唔可以再詳細一d 有少少唔明

最佳解答:

1.Ifm+n=11, m^2+n^2=99, what is m^3+n^3? Sol (m+n)^2-(m^2+n^2) =121-99 =22 mn=11 m^3+n^3 =(m+n)(m^2-mn+n^2) =(m+n)(m^2+2mn+n^2-3mn) =11*(121-33) =11*88 =968 2.A 3-digit number is subtracted from a 4-digit numberand the result is a 3-digit number. The 10 digits are all different. What is the smallestpossible result? xxxx-xxx=xxx Sol ABCD-EFG=HIJ A=1,H=2 ABCD=1000+100B+10C+D EFG=100E+10F+G HIJ=200+10I+J 1000+100B+10C+D=100E+10F+G+200+10I+J 100E+10F+10I+G+J=800+100B+10C+D B=1 =>E=9 =>H<>2 So B=0 100E+10F+10I+G+J=800+10C+D E=8 =>10F+10I+G+J=10C+D無符合解笞 So E=7 10F+10I+G+J=100+10C+D 只有 C-3,D=5,F=8,G=9,I=4,J=6符合解笞 So 1035-789=246

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m+n=11, m^2+n^2=99 m = 11 - n 121 - 22n + n ^ 2 + n ^ 2= 99 2n ^ 2 - 22n + 22 = 0 n ^ 2 - 11n + 11 = 0 ( 11 + or - sqrt 77 ) / 2 = 9.887482194 or 1.112517806
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