Question

Sum of natural number and it's reciprocal is 50/7.find the number by quadratic equations

Answer 1

Answer: 7

Explanation:

The sum of a number and its reciprocal (n +
`(1)/(n)`) is
`(50)/(7)`.

`n+(1)/(n)=(50)/(7)\\\\\text{multiply everything by 7n to clear the denominator:}\\\\(7n)n+(7n)(1)/(n)=(7n)(50)/(7)\quad \rightarrow \quad 7n^2+7=50n\\\\\text{subtract 50n from both sides:}\qquad 7n^2-50n+7=0\\\\\text{factor the quadratic equation:}\qquad (7n-1)(n-7)=0\\\\\text{apply the Zero Product Property:}\qquad 7n-1=0\quad and\quad n-7=0\\\\\text{solve each equation:}\qquad n=(1)/(7)\quad and\quad n=7`

Since n is a natural number, the fraction is not a valid solution.