When two numbers are multiplied, their product is 759; but when one is subtracted from the other, their different is 10. what are these two numbers?

x = -23 and y = -33                     or x= 23 and y = 33

Step-by-step explanation:

Let the two numbers be x and y

According to given condition

their multiplication will give 759

i.e.

x * y = 759         (i)

According to second condition

x - y = 10           (ii)

Now we have two equations which we can solve to get the values of two numbers

Now from  equation (ii) we have

x - y = 10

adding y on both sides

x - y + y = 10 + y

x = 10 + y             (iii)

Putting this value in equation (i)

x * y = 759

putting value of y

(10+y)*y=759

opening the bracket by multiplying with terms outside

10 y + y² = 759

subtracting 759 from both sides

10y + y² - 759 = 759 -759

y²+10y-759 = 0

Using mid term breaking

y²+33y-23y-759=0

using factorization

y(y+33)-23(y+33)=0

(y+33)(y-23)=0

Now

y+33= 0               and y-23=0

y= - 33                    and y=23

Putting these values in equation (iii) to get the values of x

x = 10 + y

For y = 23

x = 10 + 23

x = 33

for y= -33

x = 10 - 33

x = -23

So the solutions are

x = -23 and y = -33                     or x= 23 and y = 33