Question

求解，快。 ① 1-(a-1/1-a)^2-(a^2-a+1/a^2-2a+1) ② （x^2+3x+2/2x^2+4x）·(6x/x-1)-(2/x-1); X=2+根2

③ X+(1/X)=2 ,求X^2+1/X^2 谢谢
同志们快啊！会死人的！

Answer 1

① 1-(a-1/1-a)^2-(a^2-a+1/a^2-2a+1)
=1-(a-a²-1)/(1-a)²-(a²-a+1)/(a-1)²
=1+(a²-a+1)/(a-1)²-(a²-a+1)/(a-1)²
=1+0
=1

② （x^2+3x+2/2x^2+4x）·(6x/x-1)-(2/x-1); X=2+根2
=(x+1)(x+2)/2x(x+2)*6x/(x-1)-2/(x-1)
=3(x+1)/(x-1)-2/(x-1)
=(3x+3-2)/(x-1)
=(3x+1)/(x-1)
=(6+3√2)/(1+√2)
=(6+3√2)(√2-1)/(√2+1)(√2-1)
=6√2+6-6-3√2
=3√2

③ X+(1/X)=2 ,求X^2+1/X^2
x+1/x=2
(x+1/x)²=4
x²+2+1/x²=4
∴x²+1/x²=2