The sum of two numbers is 15. If the sum of t | vedclass

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

Question

(C) Let the two numbers be $x$ and $y$.Given: $x + y = 15$ (Equation $1$).Given: $\frac{1}{x} + \frac{1}{y} = \frac{3}{10}$ (Equation $2$).From Equati

Vedclass · Accepted Answer

$5, 10$

Vedclass · Answer

(C) Let the two numbers be $x$ and $y$.Given: $x + y = 15$ (Equation $1$).Given: $\frac{1}{x} + \frac{1}{y} = \frac{3}{10}$ (Equation $2$).From Equation $2$,we get $\frac{x + y}{xy} = \frac{3}{10}$.Substituting the value of $x + y$ from Equation $1$ into this expression: $\frac{15}{xy} = \frac{3}{10}$.Solving for $xy$: $3xy = 150$,so $xy = 50$.Now we have $x + y = 15$ and $xy = 50$.These are the roots of the quadratic equation $t^2 - (x + y)t + xy = 0$.Substituting the values: $t^2 - 15t + 50 = 0$.Factoring the quadratic: $(t - 5)(t - 10) = 0$.Thus,$t = 5$ or $t = 10$.The two numbers are $5$ and $10$.

The sum of two numbers is $15$. If the sum of their reciprocals is $\frac{3}{10}$,then find the numbers.

Similar Questions

Solve the equation $x^{2}-8x-21=0$ using the quadratic formula.

If the value of the discriminant of a quadratic equation $kx^2 - 6x + 1 = 0$ is $0$,then $k = \ldots$

The length of a rectangular garden exceeds its breadth by $6 \, m$. If the area of the garden is $216 \, m^2$,find the length and the breadth of the garden.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + x - 3 = 0$

Find the roots of the following quadratic equation by the method of completing the square: $4x^{2} + 20x + 23 = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module