The sum of a non-zero number and its reciproc | vedclass

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

Question

(B) Let the required non-zero number be $x$.Then,its reciprocal is $\frac{1}{x}$.According to the problem,their sum is $\frac{10}{3}$.So,$x + \frac{1}

Vedclass · Accepted Answer

$3$ and $\frac{1}{3}$

Vedclass · Answer

(B) Let the required non-zero number be $x$.Then,its reciprocal is $\frac{1}{x}$.According to the problem,their sum is $\frac{10}{3}$.So,$x + \frac{1}{x} = \frac{10}{3}$.Multiplying the entire equation by $3x$,we get $3x^2 + 3 = 10x$.Rearranging the terms,we get the quadratic equation $3x^2 - 10x + 3 = 0$.Factoring the quadratic equation: $3x^2 - 9x - x + 3 = 0$.$3x(x - 3) - 1(x - 3) = 0$.$(3x - 1)(x - 3) = 0$.This gives $x = \frac{1}{3}$ or $x = 3$.If the number is $3$,its reciprocal is $\frac{1}{3}$. If the number is $\frac{1}{3}$,its reciprocal is $3$.Thus,the required numbers are $3$ and $\frac{1}{3}$.

The sum of a non-zero number and its reciprocal is $\frac{10}{3}$. Find the numbers.

Similar Questions

The quadratic equation having roots $-1$ and $2$ is .... .

Find the roots of the quadratic equation using the quadratic formula:
$x^{2}-3 \sqrt{5} x+10=0$

The hypotenuse of a garden in the shape of a right triangle is $1$ metre more than twice the shortest side. If the longer side containing the right angle is $7$ metres more than the shorter side,find the sides of the garden.

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $\sqrt{2} x^{2} + 7x + 5\sqrt{2} = 0$

If the following quadratic equation has two equal and real roots,then find the value of $k$: $k x^{2} - 2 \sqrt{5} x + 4 = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module