Sum of a fraction and thrice its reciprocal is \frac{31}{6}. What is the fraction?

BA LLB Banaras Hindu University 2019 Solved Paper

Question : 127 of 170

Marks: +1, -0

Sum of a fraction and thrice its reciprocal is

\;{31}/{6}

. What is the fraction?

Solution:

Let the fraction be

\;{x}/{1}

.
According to the question,

\;{x}/{1}+3(\;{1}/{x})=\;{31}/{6}

⇒ \;\; \;{x^{2}+3}/{x}=\;{31}/{6}

⇒ \;\; 6 x^{2}+18=31 x

⇒ \;\; 6 x^{2}-31 x+18=0

⇒ 6 x^{2}-4 x-27 x+18=0

⇒ 2 x(3 x-2)-9(3 x-2)=0

⇒ \;\; (2 x-9)(3 x-2)=0

⇒ \;\; x=\;{9}/{2}, \;{2}/{3}

But

\;{2}/{3}

is not in options.
Hence, required fraction

=\;{9}/{2}

Go to Question:

Prev Question

Next Question