[Toán 9]Toán violympic

I

iamadream

Câu 5 :
Có :
[tex] 3a^2+5ab+3b^2=353 \\ \Leftrightarrow 3(a+b)^2-ab=353 \Rightarrow ab = 3(a+b)^2-353 \\ P=a^2+b^2 \\ =(a+b)^2-2ab \\ =(a+b)^2 -2[3(a+b)^2-353] \\ = -5(a+b)^2 + 706 \leq 706 \\ \Rightarrow {Max}_{P}=706 [/tex]
 
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