A fraction is greater than twice its reciproc | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the fraction be $x$.According to the problem,the fraction is greater than twice its reciprocal by $\frac{7}{15}$.So,the equation is: $x - 2(\f

Vedclass · Accepted Answer

$\frac{5}{3}$

Vedclass · Answer

(B) Let the fraction be $x$.According to the problem,the fraction is greater than twice its reciprocal by $\frac{7}{15}$.So,the equation is: $x - 2(\frac{1}{x}) = \frac{7}{15}$.Multiply by $15x$ to clear the denominators: $15x^2 - 30 = 7x$.Rearrange into a standard quadratic equation: $15x^2 - 7x - 30 = 0$.Factor the quadratic equation: $15x^2 - 25x + 18x - 30 = 0$.$5x(3x - 5) + 6(3x - 5) = 0$.$(5x + 6)(3x - 5) = 0$.This gives $x = \frac{5}{3}$ or $x = -\frac{6}{5}$.Comparing with the given options,the correct fraction is $\frac{5}{3}$.

$A$ fraction is greater than twice its reciprocal by $\frac{7}{15}$. What is the fraction?

Similar Questions

The sum of a non-$zero$ number and twice its reciprocal is $\frac{33}{4}$. Find the number.

If the sum of two numbers is multiplied by each number separately,the products so obtained are $247$ and $114$. The sum of the numbers is

How many numbers up to $200$ are divisible by both $2$ and $3$?

$(13.95)^{2} - (15.04)^{2} + (18.08)^{2} - 32.64 = ?$

On dividing a number by $38$, we get $90$ as quotient and $19$ as remainder. What is the number?

Vedclass Test Series

Exam Paper Generator

Online Exam Module