Question

qual o valor mínimo do produto
P=(1+ 1/x).(1+ 1/y) ,sabendo que x+y=1?

Answer 1

$P=(1+\frac{1}{x}) ( 1+\frac{1}{y} ) \\ \\ P=(\frac{x+1}{x}) ( \frac{y+1}{y} ) \\ \\ P=\frac{xy+x+y+1}{xy} \\ \\ P=\frac{xy+1+1}{xy}\\ \\ P=\frac{xy+2}{xy} \\ \\ P=\frac{xy}{xy}+\frac{2}{xy} \\ \\ P=1+\frac{2}{xy}$