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The sum of two positive numbers is 4 and the sum of their squares is 28. What are the two numbers?

 Mar 7, 2020
 #1
avatar+21725 
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x+y = 4        can only be    1 3     or   2  2    which would not satisfy the next equation

 

x^2 + y^2 = 28               Are you sure they are both positive?

 Mar 7, 2020
 #2
avatar+288 
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So sum of two positive numbers is 4, and sum of their squares is 28.

 

Only possible numbers are 1 and 3, and 2 and 2. 0, 4 wouldn't work because square of 0 is 0.

 

1 + 3 = 4 

1^2 = 1

3^2 = 9

1+9 = 10.

(1,3) doesn't work.

 

2 + 2 = 4.

2^2 = 4

2^2 = 4

4+4 = 8.

 

(2,2) doesn't work.

 

Nothing positive works... so unless they're negative, the problem has no answer.

 Mar 7, 2020

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