+0  
 
0
58
3
avatar

When 125 is added to a number, it becomes a perfect square. When 176 is added to that same number, it also becomes a perfect square. What is the number?

 Feb 23, 2020
 #1
avatar+109450 
+1

a^2 - b^2  =  ([176+ n] - [125 +n])

 

a^2  - b^2  =  176 - 125

 

a^2 - b^2  =  51

 

Note  that   if   a  =10   and b = 7  this is true  because     10^2  - 7^2  =  100 - 49  - 51

 

So  a^2 =  100     and  b^2 =  49

 

So

 

100 - 176   =  n  =   -76

49  - 125  = = n  = -76

 

So....the  number  is   -76

 

 

 

cool cool cool

 Feb 23, 2020
 #2
avatar+18910 
+1

Another way to do this problem:

 

x + 125  =  a2                                                        x + 176  =  b2

x + 176  =  b2                                                       x + 125  =  a2

Subtracting the first equation from the second:           51  =  b2 - a2

                                                           factoring:        17·3  =  (b + a)(b - a)

This means that  b = 10  and  a = 7

So:  x + 125  =  a2      --->     x + 125  =  72     --->     x + 125  =  49     --->     x  =  -76

       x + 176  =  b2     --->     x + 176  =  102    --->     x + 176  =  100   --->     x  =  -76

 Feb 23, 2020
 #3
avatar+531 
+2

When 125 is added to a number, it becomes a perfect square. When 176 is added to that same number, it also becomes a perfect square. What is the number?

 

500 +125 = 625       sqrt(625) = 25

500 + 176 = 676      sqrt(676) = 26  indecision

 Feb 23, 2020

14 Online Users

avatar