Toán Lớp 7: Cho $\frac{a}{b}$ = $\frac{c}{d}$ CMR
a) $\frac{ab}{cd}$ = $\frac{a^2 + b^2}{c^2 + d^2}$
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Toán Lớp 7: Cho $\frac{a}{b}$ = $\frac{c}{d}$ CMR
a) $\frac{ab}{cd}$ = $\frac{a^2 + b^2}{c^2 + d^2}$
Comments ( 2 )
Đặt:\dfrac{a}{b} = \dfrac{c}{d} = k \Leftrightarrow \left\{ \begin{array}{l}
a = b.k\\
c = d.k
\end{array} \right.\left( {k \ne 0} \right)\\
\dfrac{{ab}}{{cd}} = \dfrac{{b.k.b}}{{d.k.d}} = \dfrac{{{b^2}}}{{{d^2}}}\\
\dfrac{{{a^2} + {b^2}}}{{{c^2} + {d^2}}} = \dfrac{{{{\left( {bk} \right)}^2} + {b^2}}}{{{{\left( {dk} \right)}^2} + {d^2}}} = \dfrac{{{b^2}\left( {{k^2} + 1} \right)}}{{{d^2}\left( {{k^2} + 1} \right)}} = \dfrac{{{b^2}}}{{{d^2}}}\\
Vậy\,\dfrac{{ab}}{{cd}} = \dfrac{{{a^2} + {b^2}}}{{{c^2} + {d^2}}}
\end{array}$