Question

如果a^2+b^2/2ab=2,求代数式7ab/(a^2+b^2)+(3a^2+5ab+3b^2)/6ab的值

Answer 1

(a^2+b^2)/2ab = 2

a^2+b^2 = 42ab

7ab/(a^2+b^2)+(3a^2+5ab+3b^2)/6ab

=7ab/(a^2+b^2) + [3(a^2+b^2)+5ab]/6ab

=7ab/(4ab)+(12ab+5ab)/(6ab)

=7/4 +17/6

=55/12