1.分解 (X+1)(2x+1)(3x-1)(4X-1)-36x^4 2. 求 根號95x99x101x105+144國中 回應 crazytrquan Re: 這題幫忙解一下 2008-02-13 16:54 1.原式=[(x+1)(3x-1)][(2x+1)(4x-1)]-36x^4 =(-1+2x+3x^2)(-1+2x+8x^2)-36x^4 =(-1+2x)^2+11x^2(-1+2x)+24x^4-36x^4 =(-1+2x)^2+11x^2(-1+2x)-12x^4 =(-1+2x+12x^2)(-1+2x-x^2) =-(12x^2+2x-1)(x-1)^2 2.令x=100,原式=根號((x-5)(x-1)(x+1)(x+5)+144) =根號((x^2-25)(x^2)+144) =根號(x^4-26x^2+169) =根號((x^2-13)^2) =x^2-13=10000-13=9987
crazytrquan Re: 這題幫忙解一下 2008-02-13 16:54 1.原式=[(x+1)(3x-1)][(2x+1)(4x-1)]-36x^4 =(-1+2x+3x^2)(-1+2x+8x^2)-36x^4 =(-1+2x)^2+11x^2(-1+2x)+24x^4-36x^4 =(-1+2x)^2+11x^2(-1+2x)-12x^4 =(-1+2x+12x^2)(-1+2x-x^2) =-(12x^2+2x-1)(x-1)^2 2.令x=100,原式=根號((x-5)(x-1)(x+1)(x+5)+144) =根號((x^2-25)(x^2)+144) =根號(x^4-26x^2+169) =根號((x^2-13)^2) =x^2-13=10000-13=9987
回應
crazytrquan
Re: 這題幫忙解一下
2008-02-13 16:54=(-1+2x+3x^2)(-1+2x+8x^2)-36x^4
=(-1+2x)^2+11x^2(-1+2x)+24x^4-36x^4
=(-1+2x)^2+11x^2(-1+2x)-12x^4
=(-1+2x+12x^2)(-1+2x-x^2)
=-(12x^2+2x-1)(x-1)^2
2.令x=100,原式=根號((x-5)(x-1)(x+1)(x+5)+144)
=根號((x^2-25)(x^2)+144)
=根號(x^4-26x^2+169)
=根號((x^2-13)^2)
=x^2-13=10000-13=9987