Question

已知x=3+2根号2,求x^2+x^2分之1+3(x+x分之1)-4的值

Answer 1

x²=(3+2√2)²=17+12√2,

1／x=1/(3+2√2)=(3-2√2),

√x=√(3+2√2)=√(1²+2√2+(√2)²)=1+√2

原式=x²+√x+3x+3/x-4=17+12√2+1+√2+3(3-2√2)-4=23-7√2