Question

已知x=1/(3的平方根+2的平方根),求x^5+x^4-10x^3-10x^2+2x+1的值

Answer 1

x=1/(√3 +√2)= √3 -√2

x^2=5 -2 √6

x^4=49 -20 √6

x^3=(√3 -√2)(5 -2 √6) =9 √3 -11 √2

x^5=(√3 -√2)(49 -20 √6)=89 √3 - 109 √2

x^5+x^4-10x^3-10x^2+2x+1 = 89 √3 - 109 √2 + 49 -20 √6

- 90 √3 + 110 √2 - 50 + 20 √6 + 2√3 - 2√2 +1 = √3 -√2