Toán Lớp 7: Cho a/c=c/d=b/d.CMR:a ³+c ³-b ³/c ³+b ³-d ³=a/d
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Toán Lớp 7: Cho a/c=c/d=b/d.CMR:a ³+c ³-b ³/c ³+b ³-d ³=a/d
Giúp Tớ nhé!Thanks
Comments ( 1 )
\dfrac{a}{c} = \dfrac{c}{b} = \dfrac{b}{d} = k\\
\Leftrightarrow \left\{ \begin{array}{l}
a = c.k\\
c = b.k\\
b = d.k
\end{array} \right.\\
\Leftrightarrow a = \left( {b.k} \right).k = b.{k^2} = \left( {d.k} \right).{k^2} = d.{k^3}\\
\Leftrightarrow \dfrac{a}{d} = {k^3}\\
+ )\dfrac{{{a^3} + {c^3} – {b^3}}}{{{c^3} + {b^3} – {d^3}}} = \dfrac{{{c^3}{k^3} + {b^3}{k^3} – {d^3}{k^3}}}{{{c^3} + {b^3} – {d^3}}}\\
= \dfrac{{\left( {{c^3} + {b^3} – {d^3}} \right).{k^3}}}{{{c^3} + {b^3} – {d^3}}} = {k^3}\\
\Leftrightarrow \dfrac{{{a^3} + {c^3} – {b^3}}}{{{c^3} + {b^3} – {d^3}}} = \dfrac{a}{d}\left( { = {k^3}} \right)
\end{array}$