SOLUTION: Two numbers differ by 6 and their reciprocals differ by 8/15.Find the numbers

Algebra.Com
Question 132604: Two numbers differ by 6 and their reciprocals differ by 8/15.Find the numbers
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!
First number:
Second number:

The two numbers differ by 6: We'll just assume that

The reciprocal of the first number: , and because of ,
The reciprocal of the second number: , and because of ,


Their reciprocals differ by 8/15: Since we have assumed that , , so

Re-write the first equation to solve it for x:


Substitute this expression for x into the second equation in place of x.


Multiply both sides by 15:


Lowest common denominator is just the product of the two denominators since there are no common factors. So:



Distribute and collect like terms all on the left:



Solve the numerator expression for 0, remembering to exclude 0 and -6 as values not in the domain of the function in terms of y.



Divide by -2:


Factor:
, so y = 1.5 or y = -7.5

y = 1.5 => x = 7.5 because , so:

and the first root checks.

y = -7.5 => x = -1.5 because , so:

and the second root checks.

RELATED QUESTIONS

Two positive numbers differ by 6, and their squares differ by 96. Find the... (answered by ankor@dixie-net.com)
two positive numbers differ by 11, and their square roots differ by 1. Find the... (answered by solver91311)
Two positive numbers differ by 11, and their square roots differ by 1. Find the... (answered by ankor@dixie-net.com)
Two positive numbers differ by 11, and their square roots differ by 1. Find the... (answered by Alan3354)
Two positive numbers differ by 5 and their square roots differ by 1. Find the... (answered by Alan3354)
Two positive numbers differ by 11, and their square roots differ by 1. Find the... (answered by solver91311)
4. Two numbers differ by 9 and the sum of their reciprocals is 5/12. Find the numbers. (answered by math_tutor2020)
The real numbers a and b are reciprocals the differ by 2. find their mean. (answered by ankor@dixie-net.com)
Find two positive numbers that differ by eight and whose reciprocals sum is... (answered by macston,MathLover1)