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The sum of two intergers is 5.The difference between their squares is 45 determine the numbers

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3 Answers

a+b=5
a2-b2=45
 
System of non-linear equations: (two unknowns in two equations) Solve by iterative substitution.
 
b = 5-a
a2-(5-a)2=45
a2-(25-10a+a2) = 45
10a-25=45
10a=70
a=7
 
b=5-a
b=5-7
b=-2
 
 
 
just a thought looking at the problem; what perfect square is close to 45 ?  49 !!!
49-45=4, another perfect square(2x2)
looking at 7 and 2, their sum is not 5, but 7 and -2 have a sum of 5
(7^2)-(-2)^2=49-4=45 and 7+(-2)=5