Question

The sum of a number and its reciprocal is \(\frac {65}{8}\). What is the number?

(a) 8

(b) 4

(c) 2

(d) 6

I got this question in exam.

My question is taken from Solution of Quadratic Equation by Factorisation topic in chapter Quadratic Equation of Mathematics – Class 10

Answer 1

The correct choice is (a) 8

Explanation: Let the number be x

x+\(\frac {1}{x}=\frac {65}{8}\)

\(\frac {x^2+1}{x}=\frac {65}{8}\)

8(x^2+1)=65x

8x^2+8=65x

8x^2-65x+8=0

8x^2-64x-x+8=0

8x(x-8)-1(x-8)=0

(x-8)(8x-1)=0

x=8, \(\frac {1}{8}\)

The number is 8 or \(\frac {1}{8}\).