SOLUTION: Two positive numbers differ by 4. If the sum of their reciprocals is 2/3, find these two numbers.

Question 860417: Two positive numbers differ by 4. If the sum of their reciprocals is 2/3, find these two numbers.
Answer by ben720(159) (Show Source): You can put this solution on YOUR website!
If the two positive numbers differ by four,
Let x = 1st number and x+4 = 2nd.
The sum of their reciprocals, equals

To isolate x, first multiply both sides by x(x+4)

Simplify

Multiply both sides by 3

Subtract (6x+12) from both sides

Use the quadratic formula

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=100 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2, -3. Here's your graph:

As shown by this solver, the answers for x are either 2 or -3.
However, as both numbers must be positive, it must be 2.
Your answers are 2 and 6 (as 2+4=6)
RELATED QUESTIONS
4. Two numbers differ by 9 and the sum of their reciprocals is 5/12. Find the numbers. (answered by math_tutor2020)

two positive numbers differ by 4 and square of their sum is 324. Find the... (answered by josgarithmetic)

Two positive number differ by 3. The reciprocals of the numbers add up to 7. Find the two (answered by richwmiller)

Find two positive numbers that differ by eight and whose reciprocals sum is... (answered by macston,MathLover1)

Find two positive numbers that differ by 3 and whose reciprocals have a sum of 8/9. (answered by richwmiller)

Two numbers differ by 6 and their reciprocals differ by 8/15.Find the... (answered by solver91311)

two positive whole numbers differ by 2 . If the sume of their square is 74 find the... (answered by stanbon)

If the product of two positive numbers is 8 and their sum is 6, find the sum of their... (answered by jhunjiro)

If the product of two positive numbers is 8 and their sum is 6, find the sum of their... (answered by LinnW)