Question

The sum of a fraction and thrice its reciprocal is 31/6.so find the fraction

Answer 1

3/49 is the answer. if we reciprocal 31/6 it will become 6/31 then we will devide it using 3

Answer 2

Answer:

The fraction is $\frac{x}{y}=\frac{2}{3},\frac{9}{2}$

Step-by-step explanation:

Given : The sum of a fraction and thrice its reciprocal is $\frac{31}{6}$

To find : The fraction?

Solution :

Let the fraction be $\frac{x}{y}$.

The reciprocal of the fraction is $\frac{y}{x}$

Thrice its reciprocal is $\frac{3y}{x}$

The sum of a fraction and thrice its reciprocal is $\frac{31}{6}$

$\frac{x}{y}+\frac{3y}{x}=\frac{31}{6}$

$\frac{x^2+3y^2}{xy}=\frac{31}{6}$

$6x^2+18y^2=31xy$

$6x^2-31x+18y^2=0$

$(3x - 2y)(2x - 9y) = 0$

$(3x - 2y)=0,(2x - 9y) = 0$

$\frac{x}{y}=\frac{2}{3},\frac{9}{2}$

Therefore, The fraction is $\frac{x}{y}=\frac{2}{3},\frac{9}{2}$