close
標題:
發問:
1)x^6+26x^3=27 2)144=25x^2-x^4 3)x^4+x^3-4x^2+x+1=0 更新: When did you learn this??
最佳解答:
1)x^6+26x^3=27 x^6 + 26x^3 - 27 = 0 (x^3)^2 + 26x^3 - 27 = 0 (x^3 - 1)(x^3 + 27) = 0 x^3 = 1 or x^3 = -27 x = 1 or x = -3 2)144=25x^2-x^4 x^4 - 25x^2 + 144 = 0 (x^2)^2 - 25x^2 + 144 = 0 (x^2 - 9)(x^2 - 16) = 0 x^2 = 9 or x^2 = 16 x = 3 or -3 or 4 or -4 3)x^4+x^3-4x^2+x+1=0 (x-1)(x^3 + 2x^2 - 2x - 1) = 0 (x-1)^2 (x^2 + 3x + 1) = 0 x = 1 or x = (-3±√5)/2
其他解答:
1)x^6+26x^3=27 x^6+26x^3=27 x^6+26x^3-27=0 (x^3-1)(x^3+26)=0 x^3=1 or x^3=-26 x=1 or x=(-26)^1/3 hence,the answer is x=1 or x=(-26)^1/3 2)144=25x^2-x^4 x^4-25x^2+144=0 (x^2-16)(x^2-9)=0 x^2=16 or x^2=9 x=4 or x=-4 or x=3 or x=-3 3)x^4+x^3-4x^2+x+1=0 let f(x)=x^4+x^3-4x^2+x+1 f(1)=1+1-4+1+1 f(1)=0 so,x-1 is a factor of f(x) by long division ,we have f(x)=(x-1)(x^3+2x^2-2x-1) let g(x)=x^3+2x^2-2x-1 g(1)=1+2-2-1 g(1)=0 when g(x) is divided by x-1 g(x)=(x-1)(x^2+3x+1) so,f(x)=(x-1)^2(x^2+3x+1) f(x)=0 (x-1)^2(x^2+3x+1)=0 (x-1)^2=0 or x^2+3x+1=0 x=1 or x=(-3±√5)/2 2007-01-09 20:34:19 補充： I think (1)(2)will be tought when you are form3(3) will be tought in form4.in the chapter-----FACTOR AND REMINDER
此文章來自奇摩知識+如有不便請留言告知
solve equations發問:
1)x^6+26x^3=27 2)144=25x^2-x^4 3)x^4+x^3-4x^2+x+1=0 更新: When did you learn this??
最佳解答:
1)x^6+26x^3=27 x^6 + 26x^3 - 27 = 0 (x^3)^2 + 26x^3 - 27 = 0 (x^3 - 1)(x^3 + 27) = 0 x^3 = 1 or x^3 = -27 x = 1 or x = -3 2)144=25x^2-x^4 x^4 - 25x^2 + 144 = 0 (x^2)^2 - 25x^2 + 144 = 0 (x^2 - 9)(x^2 - 16) = 0 x^2 = 9 or x^2 = 16 x = 3 or -3 or 4 or -4 3)x^4+x^3-4x^2+x+1=0 (x-1)(x^3 + 2x^2 - 2x - 1) = 0 (x-1)^2 (x^2 + 3x + 1) = 0 x = 1 or x = (-3±√5)/2
其他解答:
1)x^6+26x^3=27 x^6+26x^3=27 x^6+26x^3-27=0 (x^3-1)(x^3+26)=0 x^3=1 or x^3=-26 x=1 or x=(-26)^1/3 hence,the answer is x=1 or x=(-26)^1/3 2)144=25x^2-x^4 x^4-25x^2+144=0 (x^2-16)(x^2-9)=0 x^2=16 or x^2=9 x=4 or x=-4 or x=3 or x=-3 3)x^4+x^3-4x^2+x+1=0 let f(x)=x^4+x^3-4x^2+x+1 f(1)=1+1-4+1+1 f(1)=0 so,x-1 is a factor of f(x) by long division ,we have f(x)=(x-1)(x^3+2x^2-2x-1) let g(x)=x^3+2x^2-2x-1 g(1)=1+2-2-1 g(1)=0 when g(x) is divided by x-1 g(x)=(x-1)(x^2+3x+1) so,f(x)=(x-1)^2(x^2+3x+1) f(x)=0 (x-1)^2(x^2+3x+1)=0 (x-1)^2=0 or x^2+3x+1=0 x=1 or x=(-3±√5)/2 2007-01-09 20:34:19 補充： I think (1)(2)will be tought when you are form3(3) will be tought in form4.in the chapter-----FACTOR AND REMINDER
文章標籤
全站熱搜
留言列表
