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8*a^a*b^b=27*a^b*b^a =>(2^3*a^a*b^b)/(3^3*a^b*b^a)=1 =>(2/3)^3*(a/b)^a*(b/a)^b=1 =>(a/b)^a*(a/b)^(-b)=(3/2)^3 =>(a/b)^(a-b)=(3/2)^3 =>a/b=3/2, a-b=3 => a=9, b=6 => A=a^2+b^2=81+36=117
1 σχόλιο:
8*a^a*b^b=27*a^b*b^a =>
ΑπάντησηΔιαγραφή(2^3*a^a*b^b)/(3^3*a^b*b^a)=1 =>
(2/3)^3*(a/b)^a*(b/a)^b=1 =>
(a/b)^a*(a/b)^(-b)=(3/2)^3 =>
(a/b)^(a-b)=(3/2)^3 =>
a/b=3/2, a-b=3 => a=9, b=6 => A=a^2+b^2=81+36=117