Question

已知x等于根号2加1求4x的4次加4x的3次方减9x的2次方减2x加1的值

Answer 1

x=√2+1
x-1=√2
两边平方
x²-2x+1=2
x²-2x=1

所以4x^4+4x³-9x²-2x+1
=(4x^4-8x³)+(12x³-24x²)+(15x²-30x)+28x+1
=4x²(x²-2x)+12x(x²-2x)+15(x²-2x)+28x+1
=4x²+12x+15+28x+1
=4x²-8x+48x+16
=4(x²-2x)+48x+16
=4+48x+16
=48(√2+1)+20
=48√2+68