SOLUTION: The average of two positive integers is 134. One of the numbers is the square root of the other. Find the integers.

Question 110492: The average of two positive integers is 134. One of the numbers is the square root of the other. Find the integers.
Found 2 solutions by ganesh, stanbon:
Answer by ganesh(20) (Show Source): You can put this solution on YOUR website!

Let the numbers be x and y and y = sqrt{x}.
Therefore, y - sqrt{x}= 0--------(1)
Also, {y + x}/2 = 134
i.e., y + x = 268---------(2)
Solving (1) and (2), we get x + sqrt{x}= 268
i.e., (x-268)^2 = {-sqrt{x})^2
so, x^2 -537+ 81796 = 0
Solving these equation, we get one positive root.
That is the value of x and using this value find the value of y.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The average of two positive integers is 134. One of the numbers is the square root of the other. Find the integers.
-------------------
(x+sart(x))/2 = 134
x + sqrt(x) = 268
x + sqrt(x)-268 = 0
Let w = sqrt(x)
-----------------
x^2+w-268 = 0
w = [-1 +- sqrt(1-4*-268)]/2
w = [-1 +- sqrt(1073)]/2
w = [1 +- 32.756678...]/2
w = 16.87833935... or w = -15.87833935...
-----------
Comment:
These answers are not even close to being integers.
Check your text problem or your posting for errors.
==========================
Cheers,
Stan H.

RELATED QUESTIONS
The product of two positive integers is 45. One number is 4 more than the other. Find the (answered by richard1234)
The sum of two positive integers is 80. Find the integers if one number is 8 greater... (answered by ewatrrr,rfer)
one of two positive integers is 7 less than the other. if the product of the two integers (answered by ikleyn)
The product of two consecutive even positive integers is one hundred twenty. Find the... (answered by jim_thompson5910,KnightOwlTutor,gonzo)
The geometric mean of 2 positive numbers is the positive square root of their product.... (answered by KMST)
The difference between two positive integers is 4. If the smaller is added to the square... (answered by mananth)
Three consecutive positive integers such that the sum of the square of the first and the... (answered by mananth)
two positive numbers are consecutive even integers. if the square of the smaller... (answered by TimothyLamb,FightinBlueHens)
the sum of two positive integers is 40. find the two integers such that the product of... (answered by Alan3354)