SOLUTION: The reciprocal of 5 less than a number is 4 times the reciprocal of twice the number. Find the number.
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Question 433510: The reciprocal of 5 less than a number is 4 times the reciprocal of twice the number. Find the number.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The reciprocal of 5 less than a number
is 4 times the reciprocal of twice the number.
Find the number.
-----------------------
Let the number be "x":
Equation:
x - (1/5) = 4(1/(2x))
--------------------------
(5x-1)/5 = 2/x
-----
Cross-multiply to get:
5x^2-x = 10
5x^2-x-10 = 0
------
x = [1+- sqrt(1-4*5*-10)]/10
---
x = [1+- sqrt(1+200)]/10
---
x = [1+- sqrt(201)]/10
-----------------------------------
x = (1+sqrt(201))/10 or x = (1-sqrt(201))/10
---
x = 1.518 or x = -1.318
========================
Cheers,
Stan H.
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