Cho a/b. C/m (a+b) ^2 = a^2+b^2/c^2+d^2
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Theo đề bài:
\(\dfrac{a}{b}=\dfrac{c}{d}=h\)
\(\Rightarrow\left\{{}\begin{matrix}a=bh\\c=dh\end{matrix}\right.\)
Khi đó:
\(\left(\dfrac{a+b}{c+d}\right)^2=\left(\dfrac{bh+b}{dh+d}\right)^2=[\dfrac{b\left(h+1\right)}{d\left(h+1\right)}]^2=\dfrac{b^2}{d^2}=\dfrac{b}{d}\)
\(\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{bh^2+b^2}{dh^2+d^2}=\dfrac{b^2\left(h^2+1\right)}{d^2\left(h^2+1\right)}=\dfrac{b^2}{d^2}=\dfrac{b}{d}\)
\(\rightarrowđpcm\)
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Câu 2:
Đặt a/b=c/d=k
=>a=bk; c=dk
\(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7b^2k^2+3bk\cdot b}{11\cdot b^2k^2-8b^2}=\dfrac{7b^2k^2+3b^2k}{11b^2k^2-8b^2}=\dfrac{7k^2+3k}{11k^2-8}\)
\(\dfrac{7c^2+3cd}{11c^2-8d^2}=\dfrac{7\cdot d^2k^2+3\cdot dk\cdot d}{11\cdot d^2k^2-8d^2}=\dfrac{7k^2+3k}{11k^2-8}\)
Do đó: \(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7c^2+3cd}{11c^2-8d^2}\)
Cho a/c = b/d . C/m a^2 + c^2 / b^2 + d^2 = a^2 - c^2 / b^2 - d^2
Mình cần gấp mong mn giúp mình!=^=
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Hình như đề bài sai
cho a/b=c/d. c/m (a+b)^2/c+d = a^2+b^2/c^2+d^2