Question

高一数学题目

3，4，5三题

Answer 1

3a^2+ab-2b^2=0
(3a-2b)(a+b)=0
3a=2b或a=-b
即b/a=3/2或b/a=-1

a/b-b/a-(a^2+b^2)/ab
=(a^2-b^2)/ab-(a^2+b^2)/ab
=(a^2-b^2-a^2-b^2)/ab
=-2b^2/ab
=-2b/a

当b/a=3/2时
原式=-2*3/2=-3

当b/a=-1时
原式=-2*（-1）=2

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

(x+y+z)(-x+y+z)(x-y+z)(x+y-z)
=(x+y+z)(x-y+z)(x+y-z)(y+z-x)
=[(x+z)^2-y^2][y^2-(x-z)^2)]
=y^2((x+z)^2+(x-z)^2)-y^4-(x+z)^2(x-z)^2
=y^2(2x^2+2z^2)-y^4-(x^2-z^2)^2
=2x^2y^2+2y^2z^2-y^4-x^4-z^4+2x^2z^2
=2x^2y^2+2y^2z^2+2x^2z^2-x^4-y^4-z^4