Question

已知x=(根号2+根号3）/（根号2-根号3），求

已知x=(根号2+根号3）/（根号2-根号3），求（x²+10x+1)²+x²+20x+2的值

Answer 1

x=(√2+√3)/(√2-√3) = (√2+√3)²/(2-3) = -(√2+√3)²=-(5+2√6)
x²=[-(5+2√6)]²=49+20√6

(x²+10x+1)²+x²+20x+2
= [(49+20√6)-10(5-2√6)+1]² + 49+20√6-20(5+2√6)+2
= 0² - 51 - 20√6 +2
= -49 - 20√6

=============================================================================或者：
x=(√2+√3)/(√2-√3) = (√2+√3)²/(2-3) = -(√2+√3)²=-(5+2√6)
x²=[-(5+2√6)]²=49+20√6 = -1+10(5+2√6) = -1-10x

(x²+10x+1)²+x²+20x+2
= (-1-10x+10x+1)² -1-10x+20x+2
= 0²+10x+1
= -10(5+2√6)+1
= -49-20√6

Answer 2

xy=(2-√3)(2+√3)=4-3=1 (x+1/y)*(y+1/x)=(xy+1)/y*(xy+1)/x=(xy+1)^2/xy=(1+1)^2/2=4 ,

Answer 3