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MATH / If a, b, and c are real numbers such that a+b+c=4 and (1)/(a)+(1)/(b)+(1)/(c)=5, find the value of (a)/(b)+(b)/(a)+(a)/(c)+(c)/(a)+(b)/(c)+(c)/(b).

Problem

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problem

If a,a, b,b, and cc are real numbers such that a+b+c=4a + b + c = 4 and 1a+1b+1c=5,\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 5, find the value of ab+ba+ac+ca+bc+cb.\frac{a}{b} + \frac{b}{a} + \frac{a}{c} + \frac{c}{a} + \frac{b}{c} + \frac{c}{b}.
Plain-text mathematical notation (without MathML)
If a, b, and c are real numbers such that a+b+c=4 and (1)/(a)+(1)/(b)+(1)/(c)=5, find the value of
(a)/(b)+(b)/(a)+(a)/(c)+(c)/(a)+(b)/(c)+(c)/(b).
Original LaTeX notation
If $a,$ $b,$ and $c$ are real numbers such that $a + b + c = 4$ and $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 5,$ find the value of
\[\frac{a}{b} + \frac{b}{a} + \frac{a}{c} + \frac{c}{a} + \frac{b}{c} + \frac{c}{b}.\]

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
c73183c1-b755-5711-85ea-a957fc921fef
task_key
intermediate~5falgebra--test--c73183c1-b755-5711-85ea-a957fc921fef
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import