The sum of squares

The sum of the squares of two numbers is 233, and one of the numbers is 3, less than twice the other. Find the numbers.

Correct answer:

a =  13
b =  8

Step-by-step explanation:

a2+b2=233 a=2b3  (2b3)2+b2=233  5b212b224=0  p=5;q=12;r=224 D=q24pr=12245(224)=4624 D>0  b1,2=2pq±D=1012±4624 b1,2=1012±68 b1,2=1.2±6.8 b1=8 b2=5.6  b=b1=8 a=2 b3=2 83=13

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