A+B=5 A^3+B^3=335 求 A^2+B^2=?
2005-09-30 17:45:13 · 10 個解答 · 發問者 Anonymous in 科學 ➔ 數學
A=5-B
(5-B)^3+B^3=335
(5-B)^3+B^3-335=0
125-75B+15B^2-B^3+B^3-335=0
15B^2-75B^2-210=0
==> B=-2 or 7
當B=(-2) ==> A=7 ...結果(1)
當B=7 ==> A=(-2) ...結果(2)
所以不管結果(1)或結果(2)代入A^2+B^2
答案都是53
2005-09-30 18:05:44 · answer #1 · answered by Web-BeR 1 · 0⤊ 0⤋
好沒深度的數學題...按計算基就有了押=w=
2005-10-02 07:38:13 · answer #2 · answered by ? 2 · 0⤊ 0⤋
(A+B)3=A3+B3+3AB(A+B)53=335+3*5*ABAB=-14A2+B2=(A+B)2-2AB=25+28=53
2005-09-30 21:30:22 · answer #3 · answered by ? 7 · 0⤊ 0⤋
A^3+B^3=(A+B)^3-3AB(A+B)=335
=> 5^3-3*AB*5=335
=> AB=-14
A^2+B^2=(A+B)^2-2AB
=5^2-2*(-14)
=53
2005-09-30 19:43:37 · answer #4 · answered by 蔡春益 7 · 0⤊ 0⤋
A=5-B(5-B)^3+B^3=335-B^3+15B^2-75B+125+B^3=33515B^2-75B+125-335=0B^2-5B-14=0(B-7)(B+2)=0B=7or-2當B=7時,A=-2A^2+B^2=53----------------------當B=-2時,A=7A^2+B^2=53
2005-09-30 17:52:03 · answer #5 · answered by Anonymous · 0⤊ 0⤋
A+B=5 ....(1) A3+B3=335.....(2)由(2)A3+B3=(A+B)3-3AB(A+B).335=53-5*3AB.210=-15AB. AB=-14(1)2=A2+2AB+B2=25=A2+2*(-14)+B2.A2+B2=53為其解!
2005-09-30 17:51:33 · answer #6 · answered by Anonymous · 0⤊ 0⤋
A^3+B^3
=(A+B)(A^2-AB+B^2)
=(A+B){(A-B)^2-3AB}=335
5*(25-3AB)=335
所以AB=-14
A^2+B^2
=(A+B)^2-2AB
=25+28=53
2005-09-30 17:49:09 · answer #7 · answered by ? 3 · 0⤊ 0⤋
..........2^2 2的平方..OK?
2005-09-30 17:48:49 · answer #8 · answered by Anonymous · 0⤊ 0⤋
^是次方的意思
2005-09-30 17:48:26 · answer #9 · answered by Anonymous · 0⤊ 0⤋
^是什麼?
2005-09-30 17:45:57 · answer #10 · answered by Anonymous · 0⤊ 0⤋