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Let a and b with a>b>0 be real numbers satisfying a^2+b^2=4ab. Find a/b - b/a.

 Jul 21, 2021
 #1
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a/b - b/a = 2.

 Jul 21, 2021
 #2
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Let a and b with a>b>0 be real numbers satisfying a^2+b^2=4ab. Find a/b - b/a.

 

Hello Guest!

 

\( a^2+b^2=4ab\ |\ +2ab\\ a^2+2ab+b^2=6ab\\ (a+b)^2=6ab \)

Square numbers that are divisible by 6:

                     36,  144,  324,  576,  900

 \((a+b)\in\{\) 6,   12,    18,     24,    30

           \(a\in\{ \)6-b, 12-b, 18-b,  24-b, 30-b

           \(a\in \{\)6:b, 24:b,  54:b, 96:b, 150:b

         \(ab\in\{ \)  6,   24,    54,    96,    150

6-b=6/b       12-b=24/b      18-b=54/b   24-b=96/b  30-b=150/b

6b-b^2=6    12b-b^2=24    

 

b=4,732        b=9,464          b=14.196   b=18.928   b=23.660

a=1.268        a=2.536           a=3,894    a=5.072     a=6.340

 

I couldn't find any real numbers (integers) for a and b.

laugh  !

asinus

 
 

 Jul 21, 2021

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