1）“求(a的3次方+a的-3x次方)/(a的x次方+a的-x次方)的值”应该是“求(a的3x次方+a的-3x次方)/(a的x次方+a的-x次方)的值”的笔误吧?
原式=[a^(3x)+1/a^3x]/[a^x+1/a^x]
={[a^(6x)+1]/a^(3x)}/[(a^2x+1)/a^x]
=[(a^2x+1)(a^4x-x^2x+1)*a^x]/[a^3x*(a^2x+1)
=(a^4x-a^2x+1)/a^2x
=a^2x-1+1/a^2a
=√2+1+1+1/(√2+1)
=√2+2+(√2-1)/(√2+1)(√2-1)
=√2+2+(√2-1)/(2-1)
=2√2+1
2)和上题相仿,“x的平方+x的平方”应该是“x的平方+x的负二次方”的笔误吧?
∵[x^(1/2)+x^(-1/2)]³=x^(3/2)+3x^(1/2)+3x^(-1/2)+x^(-3/2)
∴x^(3/2)+x^(-3/2)=[x^(1/2)+x^(-1/2)]³-3[x^(1/2)+x^(-1/2)]
=3³-3*3=27-9=18
同理：x²+x﹣²=[(3²-2)²-2]=47
∴原式=（18-3）/(47-2)=15/45=1/3