[6x＾4+(x＾2-2)(3x＾2-2)+(-X＾2+2)(x＾2-2)]÷(-2x)＾2求值 ，其中x=-1/2用简便算法，不要硬算
热心网友
[6x＾4+(x＾2-2)(3x＾2-2)+(-X＾2+2)(x＾2-2)]÷(-2x)＾2=[6x＾4+(x＾2-2)(3x＾2-2-X＾2+2)]÷(-2x)＾2=[6x＾4+(x＾2-2)(2x＾2)]÷(-2x)＾2=[6x＾4+2x＾4-4x＾2]÷(-2x)＾2=(8x＾4-4x＾2)÷(4x＾2)=2x＾2-1.所以，当x=-1/2时，原式=2*(-1/2)＾2-1=1/2-1=-1/2.
热心网友
[6x^4+(x^2-2)(3x^2-2)+(-x^2+2)(x^2-2)]÷(-2x)^2={6x^4+(x^2-2)[3x^2-2-x^2+2]}÷4x^2=[6x^4+2x^2(x^2-2)]÷4(x)^2=(8x^4-4x^2)÷4x^2=2x^2-1x=1/2代入原式=2*(1/2)^2-1=-1/2
热心网友
[6x＾4+(x＾2-2)(3x＾2-2)+(-X＾2+2)(x＾2-2)]÷(-2x)＾2=-1/2
热心网友
[6x＾4+(x＾2-2)(3x＾2-2)+(-x＾2+2)(x＾2-2)]÷(-2x)＾2={6x＾4+(x＾2-2)[2x＾2+(x＾2-2)]-(x＾2-2)^2}÷(-2x)＾2=[6x＾4+2x＾2(x＾2-2)]÷4(x)＾2=(8x^2+4x^2)÷4x＾2=2x＾2-1=(1/2)-1=-1/2