己知x-1/x=-3,求xx-1/xx的值.
问题描述:
己知x-1/x=-3,求xx-1/xx的值.
答
x-1/x=(x^2-1)/x=3x^2-1/x^2=(x^4-1)/x^2=(x^2-1)(x^2+1)/x^2=3*(x^2+1)/x=3*(x+1/x)(x-1/x)^2=x^2+1/x^2-2=9 x^2+1/x^2=11(x+1/x)^2=x^2+1/x^2+2=13(x+1/x)=根号13x^2-1/x^2=正负3根号13