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標題:

解方程|x^2-6x+5|=|2x^2-3x+1|

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解方程|x^2-6x+5|=|2x^2-3x+1| thx

最佳解答:

Method I : |x^2-6x+5|=|2x^2-3x+1| =>x^2-6x+5=2x^2-3x+1 and x^2-6x+5=-(2x^2-3x+1) =>x^2+3x-4=0 and 3x^2 -3x +6=0 =>x^2+3x-4=0 and x^2-x+2=0(rejected) =>(x+4)(x-1)=0 => x=-4 or x=1 Method II : |x^2-6x+5|=|2x^2-3x+1| =>|x-5||x-1|=|2x-1||x-1| =>|x-5||x-1|-|2x-1||x-1|=0 =>|x-1| ( |x-5|-|2x-1| )= => |x-1|=0 or |x-5|= |2x-1| => x=1 or x-5= 2x-1 or x-5=1-2x => x =5 , -4 (rejected ) or 4/3 (rejeated) so x=5 2009-04-05 19:23:49 補充： => x =1 , -4 or 4/3 (rejeated) so x=1 , -4 2009-04-05 19:24:41 補充： => x =1 , -4 or 2 => x=-4, 1,2

其他解答:

1x^2-6x+51=12x^2-3x+11 1x^2-6x-12x^2+3x=-51+11 2x-6x-24x+3x=-40 -25x=-40 x=-40/-25 x=1.6|||||Solution : As |x^2-6x+5|=|2x^2-3x+1| So x^2-6x+5 = 2x^2-3x+1 or x^2-6x+5 = -(2x^2-3x+1) 0 = x^2+3x-4 3x^2-9x+6 = 0 (x = -4 or 1) x^2-3x+2 = 0 (x = 1 or 2) Therefore, x = -4, 1 or 2. Explanation : If |a|=|b| Then a = +/- b If |a|=|b|+1 Then a is not = +/-b+1 as b may be < -1 We need to set up cases in this situation. 2009-04-05 19:19:13 補充： 0 = x^2+3x-4 or 3x^2-9x+6 = 0 (x = -4 or 1) or x^2-3x+2 = 0 >>>> (x = 1 or 2)