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find the difference between two positive number

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2 Answers

a-b=4
a^2+b^2=58
a-b=4 implies a=b+4
substitute
(b+4)^2+b^2=58
b^2+8b+16+b^2=58
2b^2+8b+16=58
2b^2+8b+16-58=0
2b^2+8b-42=0
b^2+4b-21=0
(b+7)(b-3)=0
b-3=0
b=3
a-3=4
a=7
a=7,b=3
don't forget, you said two positive numbers so we stop here
A-B=4             (1)
A²+B²=58       (2)
 
(A-B)²=A²-2AB+B²=16
Substitute from equation (2)
(A-B)²=-2AB+58=16
So now have -2AB+58=16 or that -2AB=-42 or that AB=21
 
Look at A-B=4 and AB=21
Substitute A=B+4 into AB=21 and have (B+4)B=21 or that
B²+4B-21=0 which factors int (B+7)(B-3)=0 which gives that B=3 or B=-7
For B=3, A=7 and A²+B²=58
For B=-7, A=-11 and A²+B²=170 not a solution
Smaller number =3; larger number =7