X1/2次方+X1/2次方=3
1)求X+ X的-1次方 2)X3/2次方+X-3/2次方+2 —————————— X的平方+X的-2次方+3
如果已知X1/2次方+X-1/2次方=3,则可以根据 (a+b)^2=a^2+b^2+2ab (a+b)^3=a^3+b^3+3a^2b+3ab^2 计算得到 x+1/x=9-2=7 x^(3/2)+x^(-3/2)+2=27-3*3+2=20 X^2+X^(-2)+3=49-2+3=50
(1)x+1/x=(x^1/2+x^(-1/2))^2-2=9-2=7 (2)x^(3/2)+x^(-3/2)+2=(x^1/2+x^(-1/2))(x+x^(-1)-1)+2=3*(7-1)+2=18+2=20 (3)x^2+x^-2+3=(x+1/x)^2-2+3=49-2+3=50