2.4 The product of tyo numbers $$ x $$ and $$ y $$ is 60 and their sum is 15 . Show that $$ \frac{1}{x}+\frac{1}{y}=\frac{1}{4} $$.

Question

UpStudy AI · Accepted Answer

We are given that
$$
xy = 60 \quad \text{and} \quad x+y = 15.
$$

We want to show that
$$
\frac{1}{x}+\frac{1}{y}=\frac{1}{4}.
$$

Step 1: Express the sum of the reciprocals as a single fraction.
$$
\frac{1}{x}+\frac{1}{y}=\frac{y+x}{xy}.
$$

Step 2: Substitute the given values into the fraction.
$$
\frac{x+y}{xy}=\frac{15}{60}.
$$

Step 3: Simplify the fraction.
$$
\frac{15}{60}=\frac{1}{4}.
$$

Thus, we have shown that
$$
\frac{1}{x}+\frac{1}{y}=\frac{1}{4}.
$$
$$ \frac{1}{x} + \frac{1}{y} = \frac{1}{4} $$

2.4 The product of tyo numbers \( x \) and \( y \) is 60 and their sum is 15 . Show that \( \frac{1}{x}+\frac{1}{y}=\frac{1}{4} \).