Question

determinati numarul xy cu bara deasupra stiind ca : xy cu bara la a 2 - 1190 = xy cu bara

Answer 1

xy²-xy-1190=0
xy²-35xy+34xy-34·35=0
xy(xy-35)+34(xy-35)=0
(xy-35)(xy+34)=0
xy-35=0=>xy=35
xy+34=0=>xy=-34(fals)

Answer 2

$Rezolvare~la~nivel~de~clasa~a~5-a. \\ \\ \overline{xy}^2-1190= \overline{xy} \\ \\ Deoarece~ \overline{xy} \geq 10~rezulta~ca~\overline{xy}^2 -1190 \geq 10 \Leftrightarrow \overline{xy}^2 \geq 1200 \Rightarrow \\ \\ \Rightarrow \overline{xy} \geq 35. \\ \\ \overline{xy}^2-1190 = \overline{xy} \Leftrightarrow \overline{xy}^2- \overline{xy}=1190 \Leftrightarrow \overline {xy} ( \overline{xy}-1)=1190.$

$Cum~ \overline{xy} \geq 35 \Rightarrow \overline{xy} ( \overline{xy}-1) \geq 35 \cdot 34=1190 \Leftrightarrow 1190 \geq 1190 \Rightarrow \\ \\ \Rightarrow \boxed{\overline{xy}=35}~.$