SOLUTION: Suppose that a is a positive number such that the roots of x� - ax + 1 differ exactly by 1. What is the value of a?

Question 1106560: Suppose that a is a positive number such that the roots of x� - ax + 1 differ exactly by 1. What is the value of a?
Answer by dkppathak(439) (Show Source): You can put this solution on YOUR website!
Suppose that a is a positive number such that the roots of x� - ax + 1 differ exactly by 1. What is the value of a?
roots will be a+sqrt(a^-4)/2 and a-sqrt(a^2-4)/2
difference of roots =1
a+sqrt(a^-4)/2 - a-sqrt(a^2-4)/2=1
sqrt(a^2-4)=1
a^2-4=1
a^2=1+4=5
a=plus and minus sqrt5 but it is positive number
so a= sqrt5
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