SOLUTION: The sum of the reciprocals of two consectutive intergers is 3/2.What are the intergers?

Question 414862: The sum of the reciprocals of two consectutive intergers is 3/2.What are the intergers?
Found 2 solutions by MathLover1, Gogonati:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Let the smaller integer be , then the larger one is (since they are consecutive).
Knowing that the sum of the reciprocals of these two integers is 3 / 2, we obtain an equation:

...cross multiply

.........use quadratic formula

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=3, b=1, and c=-2

Square 1 to get 1

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another answer is

So our solutions are:

or

So our solutions are:
....is not an integer, so we discard this solution
or
If the smaller integer is , then the second must be
Answer: ,

Answer by Gogonati(855) (Show Source): You can put this solution on YOUR website!
1/x+1/x+1=3/2
2(x+1)+2x=3x(x+1)
2x+2+2x=3x^2+3x
3x^2-x-2=0
{-2/3, 1} Answer:The two consecutive integers are 1 and 2
Proof: 1+1/2=3/2
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