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