1、设x=根号5 -1/2,求x4+x2+2x-12、展开(x-2)4次方3、计算(x-1)(x-2)(x-3)(x-4)
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1、设x=根号5 -1/2,求x4+x2+2x-12、展开(x-2)4次方3、计算(x-1)(x-2)(x-3)(x-4)
1、设x=根号5 -1/2,求x4+x2+2x-1
2、展开(x-2)4次方
3、计算(x-1)(x-2)(x-3)(x-4)
1、设x=根号5 -1/2,求x4+x2+2x-12、展开(x-2)4次方3、计算(x-1)(x-2)(x-3)(x-4)
1.
x=(√5-1)/2
2x+1=√5
两边平方
4x^2+4x+1=5
4x^2+4x=4
x^2+x=1
x^4+x^2+2x-1
=x^4+x^3-x^3+x^2+2x-1
=x^2(x^2+x)-x^3+x^2+2x-1
=x^2×1-x^3+x^2+2x-1
=-x^3+2x^2+2x-1
=-x^3-x^2+3x^2+2x-1
=-x(x^2+x)+3x^2+2x-1
=-x×1+3x^2+2x-1
=3x^2+x-1
=3x^2+3x-2x-1
=3(x^2+x)-2x-1
=3×1-2x-1
=-2x+2
=-2(√5-1)/2+2
=-√5+1+2
=3-√5
2.
(x-2)^4
=[(x-2)^2]^2
= (x^2-4x+4)^2
=[(x^2-4x)+4]^2
=(x^2-4x)^2+8(x^2-4x)+16
=x^4-8x^3+16x^2+8x^2-32x+16
3.
(X-1)(X-2)(X-3)(X-4)
=(X-1)(X-4) (X-2)(X-3)
=(x^2-5x+4)(x^2-5x+6)
=(x^2-5x)^2+10(x^2-5x)+24
=x^4-10x^3+25x^2+10x^2-50x+24
=x^4-10x^3+35x^2-50x+24
=x^4-8x^3+24x^2-32x+16
x=(√5-1)/2
2x+1=√5
4x^2+4x+1=5
4x^2+4x=4
x^2+x=1
x^4+x^2+2x-1
=x^4+x^3-x^3+x^2+2x-1
=x^2(x^2+x)-x^3+x^2+2x-1
=x^2×1-x^3+x^2+2x-1
=-x^3+2x^2+2x-1
=-x^3...
全部展开
x=(√5-1)/2
2x+1=√5
4x^2+4x+1=5
4x^2+4x=4
x^2+x=1
x^4+x^2+2x-1
=x^4+x^3-x^3+x^2+2x-1
=x^2(x^2+x)-x^3+x^2+2x-1
=x^2×1-x^3+x^2+2x-1
=-x^3+2x^2+2x-1
=-x^3-x^2+3x^2+2x-1
=-x(x^2+x)+3x^2+2x-1
=-x×1+3x^2+2x-1
=3x^2+x-1
=3x^2+3x-2x-1
=3(x^2+x)-2x-1
=3×1-2x-1
=-2x+2
=-2(√5-1)/2+2
=-√5+1+2
=3-√5
(x-2)^4
=[(x-2)^2]^2
= (x^2-4x+4)^2
=[(x^2-4x)+4]^2
=(x^2-4x)^2+8(x^2-4x)+16
=x^4-8x^3+16x^2+8x^2-32x+16
(X-1)(X-2)(X-3)(X-4)
=(X-1)(X-4) (X-2)(X-3)
=(x^2-5x+4)(x^2-5x+6)
=(x^2-5x)^2+10(x^2-5x)+24
=x^4-10x^3+25x^2+10x^2-50x+24
=x^4-10x^3+35x^2-50x+24
=x^4-8x^3+24x^2-32x+1
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