SOLUTION: The sum of 2 numbers is 20, their product is 10. If the sum of their reciprocals is a, find a?

Algebra.Com
Question 1071818: The sum of 2 numbers is 20, their product is 10. If the sum of their reciprocals is a, find a?
Found 4 solutions by josgarithmetic, stanbon, KMST, ikleyn:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
Two numbers, x and y







discrim,









The two numbers are .


SUM OF THE RECIPROCALS


, to rationalize denominator and get common denominator

, uses Difference Of Squares






Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
The sum of 2 numbers is 20, their product is 10. If the sum of their reciprocals is a, find a?
----
x + y = 20
x*y = 10
-------
x(20-x) = 10
x^2 - 20x + 10 = 0
----
x = 19.487
y = 0.513
====
a = 1/x + 1/y = 2
-----------------
Cheers,
Stan H.
-----------------
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
Let and be the two numbers.
We are told that
and ,
and we are asked to find
.
From we get
and .
Substituting those expressions
for and
in , we get


Does the expression in brackets look familiar?
It is .
So, ,
, and
.
You could solve for and ,
but it will be ugly.
Answer by ikleyn(52884)   (Show Source): You can put this solution on YOUR website!
.
.
You are given 

x + y = 20,  xy = 10.


You are asked about .


 =  = .


Now replace the numerator by 20, and replace the denominator by 10. You will get


 =  =  = 2.

Solved. You do not need solve any equations.


---------------------------------

What "josgarithmetic" is doing here is demonstration of his mathematical illiteracy.

He is doing here day after day despite my warnings.



RELATED QUESTIONS

The sum of 2 numbers is 20, their product is 10. If the sum of their reciprocals is a,... (answered by ankor@dixie-net.com,ikleyn)
if the sum of two numbers is 10 and their product is 5 what is the sum of their... (answered by josgarithmetic)
If the product of two positive numbers is 8 and their sum is 6, find the sum of their... (answered by jhunjiro)
If the product of two positive numbers is 8 and their sum is 6, find the sum of their... (answered by LinnW)
The product of two numbers is 5 and the sum of their reciprocals is 9/10. Find the... (answered by checkley75)
The sum of two numbers is 20. Find the numbers and their product if their product is a... (answered by math_helper)
A number is thrice another number. The sum of their reciprocals is 4. Find the... (answered by swincher4391)
Two numbers have a sum of 5, and the sum of their reciprocals is 1. Find the exact... (answered by josgarithmetic)
the sum of 2 whole numbers is 9 and the sum of their reciprocals is 1/2. find the... (answered by lwsshak3)