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

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(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

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$5, 10$

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(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.

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