solve the equation

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solve the equation
a2+b2-4a+2b+1=0……………(1)
a2+b2+4a+8b+11=0…………(2)
(2)-(1): a2+b2+4a+8b+11-(a2+b2-4a+2b+1)=08a+6b+10=0
a=(-3b-5)/4 --- (3)
(1)+(2): a2+b2+4a+8b+11+(a2+b2-4a+2b+1)=02a2+2b2+10b+12=0a2+b2+5b+6=0 --- (4)

Subst. (3) into (4):
((-3b-5)/4)2+b2+5b+6=025b2+110b+121=0
b2+4.4b+4.84=0(b+2.2)2=0
b= -2.2 --- (5)Subst. (5) into (3):
a= ( (-3)(-2.2) - 5 )/4a= 0.4

a^2+b^2-4a+2b+1=0……………(1)
a^2+b^2+4a+8b+11=0…………(2)

from (1),
a^2+b^2-4a+2b+1=0
a^2+b^2 = 4a-2b-1……………(3)

from (2),
a^2+b^2+4a+8b+11=0
a^2+b^2 = -4a-8b-11…………(4)

combine (3) & (4),
4a-2b-1 = -4a-8b-11
8a+6b+10 = 0
b = -(8a+10)/6
b = -(4a+5)/3

put b into (1),
a^2+b^2-4a+2b+1=0
a^2 +[-(4a+5)/3]^2 -4a +2[-(4a+5)/3] +1 =0
a^2 +[(4a+5)/3]^2 -4a +2[-(4a+5)/3] +1 =0
a^2 +([(4a+5)^2]/[3^2]) -4a +2[-(4a+5)/3] +1 =0
a^2 +([(4a)^2 +2(4)(5)a +(5)^2] / [9]) -4a +2[-(4a+5)/3] +1 =0
a^2 +([16a^2 +40a +25] / 9) -4a +2[-(4a+5)/3] +1 =0
9a^2 +[16a^2 +40a +25] -9(4a) +9(2[-(4a+5)/3]) +9(1) =0
9a^2 +16a^2 +40a +25 -36a +(18[-(4a+5)/3]) +9 =0
9a^2 +16a^2 +40a +25 -36a +(6[-(4a+5)]) +9 =0
9a^2 +16a^2 +40a +25 -36a -24a-30 +9 =0
25a^2 -20a +4 =0
(-5a-2)^2 = 0
-5a-2 = 0
a = -2/5

put a into (2),
a^2+b^2+4a+8b+11=0
(-2/5)^2 + b^2 +4(-2/5) +8b +11 = 0
(4/25) + b^2 +(-8/5) +8b +11 = 0
(4) + 25(b^2) + 5(-8) +25(8b) +25(11) = 0
4 + 25(b^2) -40 +200b +275 = 0
25(b^2) +200b +239 = 0

by formula,
b = (-200 (+/-) [(200^2) -4(25)(239)]^(1/2)) / 2(25)
= (-200 (+/-) [(40000 -23900)^(1/2)]) / 50
= (-200 (+/-) [(16100)^(1/2)]) / 50
= (-200 +[(16100)^(1/2)]) / 50 or = (-200 -[(16100)^(1/2)]) / 50

自己咁機啦

If (2) - (1),

a2+b2+4a+8b+11-(a2+b2-4a+2b+1)=0
8a+6b+10=0
4a+3b+5=0
a= (-3b-5) / 4 ..............(i)

If (1) + (2),
2a2 + 2b2 + 10b + 12 = 0
2(a2 + b2) +10b = -12
a2 + b2 + 5b = -6-----------------(ii)

Sub. (i) into (ii)

[(-3b-5)2 ] / 16 + b2 + 5b = -6
(9b2 - 30b + 25) / 16 + b2 + 5b = -6
9b2 - 30b + 25 + 16b2 + 80b = -96
25b2 + 50b + 121 = 0
(5b + 5)2 + 96 = 0
(5b + 5)2 = -96
Since any square of any number will not be a minus number, therefore, this equation is undefined! Cannot be Solved!

2007-12-29 15:55:27 補充：
Sorry, 原來係我計錯, Eddie HUI
答案先對!Sub. (i) into (ii)[(-3b-5)2 ] / 16 b2 5b = -6(9b2 30b 25) / 16 b2 5b = -6 (應該係 30b, 所以錯左一個加減符號會影響結果!)25b2 110b 121 = 0 b2 4.4b 4.84 = 0........................... 之後步驟同 Eddie HUI 的都係一樣!a=0.4 , b= -2.2