Chọn đẳng thức sai trong các đẳng thức dưới đây.
Suy nghĩ và trả lời câu hỏi trước khi xem đáp án
Lời giải:
Báo sai\(+)\,\left( { - {x^n}{y^n}{z^n}} \right):{x^{n - 1}}{y^{n - 2}}{z^{n - 3}}\)
\( = - \left( {{x^n}:{x^{n - 1}}} \right).\left( {{y^n}:{y^{n - 2}}} \right)\)\(.\left( {{z^n}:{z^{n - 3}}} \right)\)
\( = - {x^{n - \left( {n - 1} \right)}}.{y^{n - \left( {n - 2} \right)}}.{z^{n - \left( {n - 3} \right)}} \)
\(= - x{y^2}{z^3}\)
\(+)\,\left( { - \dfrac{2}{3}{x^{n + 1}}{y^{n + 2}}} \right)\)\(:\left( { - \dfrac{3}{4}{x^n}{y^{n - 8}}} \right)\)
\( = \left[ {\left( { - \dfrac{2}{3}} \right):\left( { - \dfrac{3}{4}} \right)} \right]\)\(.\left( {{x^{n + 1}}:{x^n}} \right).\left( {{y^{n + 2}}:{y^{n - 8}}} \right)\)
\( = \left( {\dfrac{{ - 2}}{3}.\dfrac{{ - 4}}{3}} \right)\)\(.{x^{n + 1 - n}}.{y^{n + 2 - \left( {n - 8} \right)}} \)
\(= \dfrac{8}{9}x{y^{10}}\)
\(+)\,{x^{2007}}{y^{2008}}{z^{2009}}\)\(:\left( { - \dfrac{1}{5}{x^2}yz} \right)\)
\( = 1:\left( { - \dfrac{1}{5}} \right).\left( {{x^{2007}}:{x^2}} \right)\)\(.\left( {{y^{2008}}:y} \right)\)\(.\left( {{z^{2009}}:z} \right)\)
\( = 1.\left( {\dfrac{{ - 5}}{1}} \right)\)\(.{x^{2007 - 2}}.{y^{2008 - 1}}.{z^{2009 - 1}} \)
\(= - 5{x^{2005}}{y^{2007}}{z^{2008}}\)
\(+)\,\left( { - 5{x^5}{y^{10}}{z^{15}}{t^{20}}} \right)\)\(:\left( { - \dfrac{2}{3}{x^2}{y^4}{z^6}} \right)\)
\( = \left[ {\left( { - 5} \right):\left( {\dfrac{{ - 2}}{3}} \right)} \right]\)\(.\left( {{x^5}:{x^2}} \right)\)\(.\left( {{y^{10}}:{y^4}} \right)\)\(.\left( {{z^{15}}:{z^6}} \right).{t^{20}}\)
\( = \left( { - 5} \right).\left( {\dfrac{{ - 3}}{2}} \right)\)\(.{x^{5 - 2}}.{y^{10 - 4}}.{z^{15 - 6}}.{t^{20}}\)
\( = \dfrac{{15}}{2}{x^3}{y^6}{z^9}{t^{20}} \)
\(= 7\dfrac{1}{2}{x^3}{y^6}{z^9}{t^{20}}\)
