Question

已知X=(2的算术平方根+1)/2,求代数式4x^4+4x^3-9x^2-2x+1的值.(4x^4即4x的4次方)

Answer 1

X=(2的算术平方根+1)/2

x^2=(2+2√3+1)/4

4x^2=(3+2√3)

4x^4+4x^3-9x^2-2x+1

=4x^2（x^2+x-9/4)-2x+1

=(3+2√3)((3+2√3)/4+(√2+1/2-9/4)-2(√2+1/2)+1

=(3+2√3)(-4+2√3+2√2)/4-2(√2+1/2)+1

=(3+2√3)(-2+√3+√2)/2-√2-1+1

=(-6+3√3+3√2-4√3+6+2√6)/2-√2

=(3√2-√3+2√6)/2-√2

=(√2-√3+2√6)/2