作业帮若x等于根号5减1,求x^5+2x^4-5x^3-x^2+6x-5的值
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若x等于根号5减1,求x^5+2x^4-5x^3-x^2+6x-5的值
若x等于根号5减1,求x^5+2x^4-5x^3-x^2+6x-5的值
若x等于根号5减1,求x^5+2x^4-5x^3-x^2+6x-5的值
x=根号5-1,则有x+1=根号5
(x+1)²=5,x²+2x+1=5,x²+2x=4
x^5+2x^4-5x^3-x^2+6x-5
=x³(x²+2x)-5x³-x²+6x-5
=4x³-x³-x²+6x-5
=-x³-x²+6x-5
=-x(x²+2x)+x²+6x-5
=-4x+x²+6x-5
=x²+2x-5
=4-5
=-1
因为x=根号5减1
所以x+1=根号5
所以(x+1)^2=5
即x^2+2x-4=0
x^5+2x^4-5x^3-x^2+6x-5=(x^2+2x-4)(x^3-x+1)-1
=0-1=-1
x=√5-1
x+1=√5
(x+1)^2=5
x^5+2x^4-5x^3-x^2+6x-5
=x^5+2x^4+x^3-6x^3-x^2+6x-5
=x^3(x^2+2x+1)-6x^3-x^2+6x-5
=x^3(x+1)^2-6x^3-x^2+6x-5
=5x^3-6x^3-x^2+6x-5
=-x^3-x^2+...
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x=√5-1
x+1=√5
(x+1)^2=5
x^5+2x^4-5x^3-x^2+6x-5
=x^5+2x^4+x^3-6x^3-x^2+6x-5
=x^3(x^2+2x+1)-6x^3-x^2+6x-5
=x^3(x+1)^2-6x^3-x^2+6x-5
=5x^3-6x^3-x^2+6x-5
=-x^3-x^2+6x-5
=-x^3-2x^2-x+x^2+7x-5
=-x(x^2+2x+1)+x^2+7x-5
=-x(x+1)^2+x^2+7x-5
=-5x+x^2+7x-5
=x^2+2x-5
=(x+1)^2-6
=5-6=-1
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