Cho a/b = c/d. CMR
1) a-c/a+c= b-d/b+d
2) a^2020- b^2020/a^2020+ b^2020 = c^2020- d^2020/c^2020+ d^2020
Nhìn hơi dối thoy chứ đọc kĩ thì đầu bài ngắn lắm, giup mk vs mai mk nộp r ạ mơn nòk
Cho a/b = c/d. CMR
1) a-c/a+c= b-d/b+d
2) a^2020- b^2020/a^2020+ b^2020 = c^2020- d^2020/c^2020+ d^2020
Nhìn hơi dối thoy chứ đọc kĩ thì đầu bài ngắn lắm, giup mk vs mai mk nộp r ạ mơn nòk
Các bước giải:
\(\begin{array}{l}
1)\,\dfrac{a}{b} = \dfrac{c}{d} = \dfrac{{a – c}}{{b – d}} = \dfrac{{a + c}}{{b + d}}\\
\Rightarrow \dfrac{{a – c}}{{a + c}} = \dfrac{{b – d}}{{b + d}}\\
2)\dfrac{a}{b} = \dfrac{c}{d} \Rightarrow \dfrac{{{a^{2020}}}}{{{b^{2020}}}} = \dfrac{{{c^{2020}}}}{{{d^{2020}}}}\\
\Rightarrow \dfrac{{{a^{2020}} – {b^{2020}}}}{{{b^{2020}}}} = \dfrac{{{c^{2020}} – {d^{2020}}}}{{{d^{2020}}}}\\
\Rightarrow \dfrac{{{a^{2020}} – {b^{2020}}}}{{{c^{2020}} – {d^{2020}}}} = \dfrac{{{b^{2020}}}}{{{d^{2020}}}}\\
Lai\,co:\dfrac{{{a^{2020}}}}{{{b^{2020}}}} = \dfrac{{{c^{2020}}}}{{{d^{2020}}}}\\
\Rightarrow \dfrac{{{a^{2020}} + {b^{2020}}}}{{{c^{2020}} + {d^{2020}}}} = \dfrac{{{b^{2020}}}}{{{d^{2020}}}}\\
\Rightarrow \dfrac{{{a^{2020}} – {b^{2020}}}}{{{c^{2020}} – {d^{2020}}}} = \dfrac{{{a^{2020}} + {b^{2020}}}}{{{c^{2020}} + {d^{2020}}}}\\
\Rightarrow \dfrac{{{a^{2020}} – {b^{2020}}}}{{{a^{2020}} + {b^{2020}}}} = \dfrac{{{c^{2020}} – {d^{2020}}}}{{{c^{2020}} + {d^{2020}}}}
\end{array}\)