Question

Va rog frumos,b-c.. Urgent..dau coroana

Answer 1

[tex]\text{b) Ne folosim de punctul a) ca s\u a mai simplific\u am din calcule.}\\\text{Din a) }\rightarrow x\Diamondy=(x-6)(y-6)+6\\ \text{Asociativitatea: }(x\Diamond y)\Diamond z=x\Diamond(y\Diamond z)\\\:[(x-6)(y-6)+6]\Diamond z=x\Diamond[(y-6)(z-6)+6]\\\:[(x-6)(y-6)+6-6](z-6)+6=(x-6)[(y-6)(z-6)+6-6]+6\\(x-6)(y-6)(z-6)+6=(x-6)(y-6)(z-6)+6\text{ (A)}\rightarrow\Diamond\text{ asoc.}[/tex]

$\text{c) Din a) se poate vedea c\u a:}\\6\Diamond x=(6-6)(x-6)+6=6\text{ (1)}\text{ \c si}\\x\Diamond6=(x-6)(6-6)+6=6\text{ (2)}.\\1\Diamond2\Diamond...\Diamond2016=1\Diamond2\Diamond...\Diamond6\Diamond...2016=E.\\\text{Dac\u a not\u am }A=1\Diamond2\Diamond..\Diamond5\text{ \c si }B=7\Diamond...\Diamond2016\text{ avem c\u a:}\\E=A\Diamond6\Diamond B.\\\text{Am demonstrat la b) c\u a }\Diamond\text{ este asociativ\u a, prin urmare:}\\E=(A\Diamond6)\Diamond B=(\text{din (2)})6\Diamond B=\text{(din (1))}6$