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The Square of My Age

Stage: 3 Short Challenge Level: Challenge Level:1

When you add the square of Thomas's age to Lauren's age the total is 62. When you add the square of Lauren's age to Thomas's age the total is 176. How old are Thomas and Lauren?
 
 
 
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
 
 

This problem is taken from the UKMT Mathematical Challenges.
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