Nonsensical sense

Algebra Level 1

Given that $x$ and $y$ are real numbers such that $x + y=24$ and $xy=2$ , find the value of

$\frac{1}{x} + \frac{1}{y}.$

5 solutions

Victor Loh
Aug 19, 2014

We have

$\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}$

$=\frac{24}{2}=\boxed{12},$

and we are done.

Same way Bro and i tell you its is a very smart solution

Kushagra Sahni - 6 years, 9 months ago

Dieuler Oliveira
Aug 20, 2014

$x^{2}-24x+2=0$

Reciprocal transformation:

$2x^{2}-24x+1=0$

By Vieta's:

$S=\boxed{12}.$

Long-winded, but still a pretty good solution (at the very least interesting)

Jared Low - 6 years, 6 months ago

Ashish Menon
May 29, 2016

$\begin{aligned} \dfrac{x + y}{xy} & = \dfrac{1}{x} + \dfrac{1}{y}\\ & = \dfrac{24}{12}\\ & = \color{#69047E}{\boxed{12}} \end{aligned}$

Ritam Baidya
Dec 3, 2014

simply do the LCM and solve the fraction to get 24/2 = 12

Ranjith Nrjk
Aug 16, 2014

Divide with xy on both sides