Sum And Product Given, What's Next?

Algebra Level 2

$\Large x + y =4 , \qquad xy = 5$

What is the sum of the reciprocals of $x$ and $y$ ?

The answer is 0.8.

2 solutions

Zeeshan Ali
May 7, 2016

Relevant wiki: Algebraic Manipulation - Rearranging

$\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}=\frac{4}{5}=\boxed{0.8}$ Since $x+y=4$ and $xy=5$

I did it similar, upvoted!

Paola Ramírez - 5 years ago

Andrew Trichak
May 24, 2016

$xy = 5$ implies $x = \frac{5}{y}, \ y = \frac{5}{x}$ . This gives $5 \times \left(\frac{1}{x} + \frac{1}{y} \right) = 4$ which implies the reciprocals sum to $\frac{4}{5}$ .

Nice approach, and good observation, Andrew. I upvoted your solution :)

Pranshu Gaba - 5 years ago

Sum And Product Given, What's Next?

The answer is 0.8.

2 solutions

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