SOLUTION: Hello! Could you give e chanse to have the solution of this problem? The different of two naural number is 9 and he different of their reciprocal is 9/190. Find the numbers. This

Question 202020: Hello! Could you give e chanse to have the solution of this problem?
The different of two naural number is 9 and he different of their reciprocal is 9/190. Find the numbers.
This was my way which doesn't go on:

or

Since sqrt( 3037801 ) is not an integer number (it is a so called irrational number, not reducible to fractions like m/n), further reduction of this expression will not give you an integer result.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"The difference of two natural numbers is 9" translates to

"the difference of their reciprocals is 9/190" means that

Note: if , then

Start with the first equation.

Add "y" to both sides.

Move onto the second equation

Plug in

Multiply EVERY term by the LCD to clear out the fractions.

Simplify

Distribute

Get all terms to the left side.

Combine like terms.

Notice that the quadratic is in the form of where , , and

Let's use the quadratic formula to solve for "y":

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible solutions for "y" are or

However, the problem stated that the numbers are natural. So we have to throw out

So the only answer for "y" is . This means that "x" is

========================================================================================

Answer:

So the solutions are and

So the two numbers are 19 and 10

Take note that and
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