Question

设3x²－x＝1，求9乘以x的四次方加12x³－3x²－7x＋2000的值

请先自己列一下式，没办法写上式子

Answer 1

9x^4+12x^3-3x^2-7x+2000
=(3x^2-x)(3x^2+5x+2/3)-7x+2000+2/3x
=3x^2+5x+2/3-7x+2000+2/3x (3x²－x＝1)
=3x^2-2x+2/3x+2000+2/3
=1-x+2/3x+2000+2/3 (3x²－x＝1)
=-1/3x+2001+2/3

3x²－x＝1,
x=(1+13^0.5)/6 or (1-13^0.5)/6

9x^4+12x^3-3x^2-7x+2000
=-1/3*(1+13^0.5)/6+2001+2/3
or
=-1/3*(1-13^0.5)/6+2001+2/3