[MOVED] the sum of a number and its reciprocal is 10/3

x + 1/x = 10/3
Multiply through by x and then 3.
Solve the resulting quadratic for x.
 
Re: the sum of a number and its reciprocal is 10/3. Find the

escaped_insane said:
the sum of a number and its reciprocal is 10/3. Find the #

~~steps to getting answer please!


\(\displaystyle x + \frac{1}{x} = \frac{10}{3}\)

\(\displaystyle \frac{x^2+1}{x} = \frac{10}{3}\)

You may be able to see one answer here, but, cross multiply:

\(\displaystyle 3(x^2+1)\) = 10x[/tex]

\(\displaystyle 3x^2 -10x + 3\) = 0[/tex]

Factor this and you'll see that x=3 or x= 1/3
 
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