SOLUTION: The difference between two whole numbers is 8 and the difference between their reciprocals is 1/6. Find the two numbers.

Algebra ->  Human-and-algebraic-language -> SOLUTION: The difference between two whole numbers is 8 and the difference between their reciprocals is 1/6. Find the two numbers.      Log On


   

Question 60953This question is from textbook Algebra For College Students
: The difference between two whole numbers is 8 and the difference between their reciprocals is 1/6. Find the two numbers. This question is from textbook Algebra For College Students

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
The difference between two whole numbers is 8 and the difference between their reciprocals is 1/6. Find the two numbers.
LET ONE NUMBER BE X
OTHER NUMBER = X-8
THEIR RECIPROCALS ARE 1/(X-8) AND 1/X
DIFFERENCE = 1/(X-8) -1/X = 1/6.....MULTIPLY THROUGH OUT WITH 6X(X-8)
6[{X-(X-8)}=X(X-8)
6[X-X+8]=X^2-8X
X^2-8X-48=0
X^2-12X+4X-48=0
X(X-12)+4(X-12)=0
(X-12)(X+4)=0
HENCE X=12...AND THE OTHER NUMBER IS 12-8 =4
IF NEGATIVE NUMBERS ARE ALLOWED
X=-4 AND THE OTHER NUMBER IS -4-8=-12