Question 216454
The sum of a number and its reciprocal is 25/12.  Find the number


Step 1.  Let x be the number and 1/x be its reciprocal.


Step 2.  Then, {{{x+1/x=25/12}}}  since the sum of a number and its reciprocal is 25/12.


Step 3.  Multiply 12x to both sides of the equation to get rid of the denominators.


{{{12x(x+1/x)=12x*25/12}}} 


{{{12x^2+12=25x}}}


Step 4.  Subtract 25x to put the equation in quadratic form 


{{{12x^2+12-25x=25x-25x}}}


{{{12x^2-25x+12=0}}}


Step 5.  We can use the quadratic formula given as 


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}


where a=12, b=-25, and c=12.


*[invoke quadratic "x", 12, -25, 12 ]


So {{{x=3/4}}} or {{{x=4/3}}} (reciprocals of each other)


Check...{{{3/4+4/3=9/12+16/12=25/12}}} which is a true statement.


Step 6.  ANSWER:  The number is {{{3/4}}} or {{{4/3}}} which are reciprocals of each other


I hope the above steps were helpful.


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http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit 

http://www.FreedomUniversity.TV/courses/Trigonometry.


Good luck in your studies!


Respectfully,
Dr J