(1)先化简再求值:当a=99时,[a+(1/a-1)][(1/1+a^3)-1]÷(a^3/1-a)(2)解方程:(7/x^2+x)-(3/x-x^2)=1+(7-x^2/x^2-1)(3)已知x+(1/x)=2,求x^2+(1/x^2)的值.(注:
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![(1)先化简再求值:当a=99时,[a+(1/a-1)][(1/1+a^3)-1]÷(a^3/1-a)(2)解方程:(7/x^2+x)-(3/x-x^2)=1+(7-x^2/x^2-1)(3)已知x+(1/x)=2,求x^2+(1/x^2)的值.(注:](/uploads/image/z/2002771-19-1.jpg?t=%EF%BC%881%EF%BC%89%E5%85%88%E5%8C%96%E7%AE%80%E5%86%8D%E6%B1%82%E5%80%BC%EF%BC%9A%E5%BD%93a%3D99%E6%97%B6%2C%5Ba%2B%281%2Fa-1%29%5D%5B%281%2F1%2Ba%5E3%29-1%5D%C3%B7%28a%5E3%2F1-a%29%EF%BC%882%EF%BC%89%E8%A7%A3%E6%96%B9%E7%A8%8B%EF%BC%9A%287%2Fx%5E2%2Bx%29-%283%2Fx-x%5E2%29%3D1%2B%287-x%5E2%2Fx%5E2-1%29%EF%BC%883%EF%BC%89%E5%B7%B2%E7%9F%A5x%2B%281%2Fx%29%3D2%2C%E6%B1%82x%5E2%2B%281%2Fx%5E2%29%E7%9A%84%E5%80%BC.%EF%BC%88%E6%B3%A8%EF%BC%9A)
(1)先化简再求值:当a=99时,[a+(1/a-1)][(1/1+a^3)-1]÷(a^3/1-a)(2)解方程:(7/x^2+x)-(3/x-x^2)=1+(7-x^2/x^2-1)(3)已知x+(1/x)=2,求x^2+(1/x^2)的值.(注:
(1)先化简再求值:当a=99时,[a+(1/a-1)][(1/1+a^3)-1]÷(a^3/1-a)
(2)解方程:(7/x^2+x)-(3/x-x^2)=1+(7-x^2/x^2-1)
(3)已知x+(1/x)=2,求x^2+(1/x^2)的值.
(注:
(1)先化简再求值:当a=99时,[a+(1/a-1)][(1/1+a^3)-1]÷(a^3/1-a)(2)解方程:(7/x^2+x)-(3/x-x^2)=1+(7-x^2/x^2-1)(3)已知x+(1/x)=2,求x^2+(1/x^2)的值.(注:
1.[a+1/(a-1)][1/(1+a^3)-1]÷a^3/(1-a)
=-[(a-1)/a^2+1/a^3][1/(1+a^3]
=-[(a^2-a+1)/a^3][1/(1+a^3]
=-1/[a^3(a+1)]
当a=99时,-1/[99^3(99+1)=-1/100*1/99^3=-1/97029900
(2)解方程:
(7/x^2+x)-(3/x-x^2)=1+(7-x^2/x^2-1)
7/(x^2+x)+3/(x^2-x)=1+(7-x^2)/(x^2-1)
7(x-1)/[x(x^2-1)]+3(x+1)/[x(x^2-1)]-x(7-x^2)/[x(x^2-1)=1
7x-7+3x+3-7x+x^3=x(x^2-1)=x^3-x
3x-4=-x
x=1
(3)已知x+(1/x)=2,求x^2+(1/x^2)的值.
x+1/x=2
(x+1/x)^2=4
x^2+2+1/x^2=4
x^2+1/x^2=2 .
3. (x+x²)²=1/x²+x²+2
4 =1/x²+x²+2
1/x²+x² =2