One number is three more than the other number. When the square of the smaller number is subtracted from the square of the smaller number, #45# is obtained. What are the two numbers?

Question

One number is three more than the other number.  When the square of the smaller number is subtracted from the square of the smaller number, #45# is obtained.  What are the two numbers?

Isaiah Anthony · Accepted Answer

Let the numbers be #x# and #y#. #{(x + 3 = y), ((x + y)(y - x) = 45):}# If we rearrange the first équation, we get #x - y = 3#.  Substituting, we get: #(x + (x + 3))(3) = 45# #2x + 3 = 15# #2x = 12# #x = 6# #:.#The numbers are #6# and #9#. Hopefully this helps!

Nathan Axel · Answer

I got #6 and 9# let s call our numbers #x# and #y#. We get: #x=y+3# and #(x+y)(x-y)=45# from the second we get: #x^2-y^2=45# substituting the first equation #x=y+3# we get: #(y+3)^2-y^2=45# #y^2+6y+9-y^2=45# #6y=36# #y=36/6=6# so that #x=6+3=9#

Kennedy Adams · Answer

The first number is 9, and the second number is 6.

Let #n# be the first number. The second number is therefore #n-3#. Sum of the numbers: #color(red)((n)+(n-3) = 2n-3)# Difference of the numbers: #color(blue)((n)-(n-3) = 3)# Equation: #color(red)((2n-3))color(blue)((3))=45# #2n-3=15# #2n=18# #n=9# (First number) #n-3=6# (Second number)

Ethan Adkins · Answer

undefined Let the smaller number be x and the larger number be x + 3.  
According to the given information, (x + 3)^2 - x^2 = 45.  
Expanding and simplifying the equation:  
(x^2 + 6x + 9) - x^2 = 45  
6x + 9 = 45  
6x = 36  
x = 6  
So, the smaller number is 6 and the larger number is 6 + 3 = 9.