1.

The sum of two numbers is 16 and the sum of their squares is 113. Find the numbers.

Answer»

Let the numbers be x and (15 - x). 

Then, x2 + (15 - x)2 = 113 

=> x2 + 225 + X2 - 30x = 113 

 => 2x2 - 30x + 112 = 0 

=> x2 - 15x + 56 = 0 

 => (x - 7) (x - 8) = 0 

=> x = 7 or x = 8. 

 So, the numbers are 7 and 8. 



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