Question

The sum of a number and it reciprocal is 26/5 Find the number

Answer 1

let the number be x
Therefore its reciprocal=1/x
Now
According to the given condition,
x+1/x=26/5
x²+1/x=26/5
26x=5(x²+1)
5x²+5=26x
5x²-26x+5=0
By splitting the middle term we get
5x²-25x-x+5=0
5x(x-5)-1(x-5)=0
(x-5)(5x-1)=0
Either
x-5=0. or.5x-1=0
x=5. or x=1/5
Therefore the numbers are 5 and 1/5