SOLUTION: One number is 8 more than another number. The sum of their reciprocals is 1/3. Find the two numbers.

Question 989269: One number is 8 more than another number. The sum of their reciprocals is 1/3. Find the two numbers.
Answer by themasterofcircuits(27) (Show Source): You can put this solution on YOUR website!
(1) y=x+8
(2) 1/x+1/y=1/3
Sub (1) into (2)

(1/x)+(1/(x+8))=1/3
(x+8)/(x(x+8))+(x)/(x(x+8))=1/3
(x+8)/(x^2+8x)+(x)/(x^2+8x)=1/3
2x+8/(x^2+8x)=1/3
2x+8=1/3(x^2+8x)
1/3x^2+8/3x-2x-8=0
1/3x^2+2/3x-8=0
x^2+2x-24=0
.
.
.
[x=4, x=-6]
If x=4:
y=x+8
[y=12]
If x=-6
y=x+8
y=[2]
-Aμstin

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