Question

x<3<y show that xy+3x<x²+3y​

Answer 1

$\displaystyle\bf\\~xy~+3x<x^2+3y \Leftrightarrow x^2+3y>xy+3x~|-xy-3x \Leftrightarrow\\x^2+3y-xy-3x>0 \Leftrightarrow x(x-y)-3(x-y)>0 \Leftrightarrow (x-y)(x-3)>0.\\ce~ai~scris~tu~in~enunt~x<3<y,~putem~scoate~ca~produsul~nu~este~nul,~\\si~cum~x~este~mai~mic~decat~3\implies (x-3)~este~negativ.\\x<y \implies(x-y)~este~negativ.\\si~cum~produsul~a~doua~numere~negative~are~valoarea~pozitiva~,si~produsul\\nu~este~0,~rezulta~concluzia.$