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While walking by a classroom, Linda sees two perfect squares written on a blackboard. She notices that their difference is her favorite number, 99. She also notices that there are exactly two other perfect squares between them. What is the sum of the two perfect squares on the blackboard?

 Dec 7, 2022
 #3
avatar+27 
+5

Umm, i think I can help. 

 

X and y are numbers. 

x^2 - y^2 = 99

x - y = 3

 

x = y + 3

(y + 3)^2 - y^2 = 99

y^2 + 6y + 9 - y^2 = 99

6y + 9 = 99

6y = 90

y = 15

 

x = 15 + 3

x = 18

 

Now we test. 

324 - 225 = 99 and there are 2 perfect squares between them, 256 and 289. 

SO, 324 + 225 = 549!

549

 Dec 7, 2022
edited by awesomecalculator6  Dec 7, 2022

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