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

[escaped_insane]

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

~~steps to getting answer please!

 

[TchrWill]

x + 1/x = 10/3
Multiply through by x and then 3.
Solve the resulting quadratic for x.

 

[daon]

Re: the sum of a number and its reciprocal is 10/3. Find the

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