Answer:
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
