Question

Two number differ by 3 The sum of their reciporcal is 7/10 find tge numbers

Answer 1

The numbers are 5 and 2.

Reciprocals: 5- 5/10
                     2- 2/10
(2/10)+(5/10)= 7/10
5-2= 3
 
Answer: 5 and 2

Answer 2

Comment
Let the larger number = x
Let the smaller number = y

Equations
x - y = 3                  (1)
1/x + 1/y = 7/10      (2)

Step one
solve for y
the common denominator on the left is xy So the left can be written as

$\frac{y+x}{xy}$

Then entire equation becomes

$\frac{y+x}{xy}= \frac{7}{10}$

Cross multiply
10*(x + y) = 7 * xy                         (3)

From the first equation x = 3 +y Put this into (3) 
10(3 + y + y) = 7*xy
10(3 + 2y) = 7xy               Make the same substitution on the right.10
10(3 + 2y) = 7(3 + y)*y
30 + 20y = 21y + 7y^2     Transfer the left side to the right side.
0 = 7y^2 + 21y - 20y - 30 
0=  7y^2 + y - 30              This will factor.

0 = (y - 2)(7y +15)

Step  Two
Solve for y    
y - 2 = 0
y = 2
or
7y + 15 = 0
7y = - 15
y = - 15/7
y = - 2.1428

Step Three
Solve for  x
If y = 2 then
x - y = 3
x - 2 = 3
x = 5

So one of the points is 
(5,2) Answer <<<<<<<<<<1st Answer

If y = - 2 1/7 then
x - - 2 1/7 = 3
x + 2 1/7 = 3    Subtract 2 1/7 from both sides.
x = 3 - (2 1/7)
x = 6/7

So the other point is (6/7, -2 1/7)  <<<< 2nd Answer