Question

方程log(x+1)|x^2-x-1|=1的解集

Answer 1

log(x+1,x^2-x-1)=1

log(x^2-x-1)=log(x+1)

log(x^2-x-1)-log(x+1)=0

log((x^2-x-1)/(x+1))=0

(x^2-x-1)/(x+1)=1

x^2-x-1=x+1

x^2-2x+1=3

(x-1)^2=3

x=1+sqrt(3)或x=1-sqrt(3)

解集：x∈{1+sqrt(3),1-sqrt(3)}