Cho a/b=c/d C/m
a) ab/cd=(a^2+b^2)/(c^2+d^2)
b) ac/bd=(a^2+c^2)/(b^2+d^2)
c) (7a^2+3ab)/(11a^2-8b^2)=(7c^2+3ab)/(11c^2-8d^2)
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Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\Rightarrow a=bk;c=dk\)
\(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7b^2k^2+3b^2k}{11b^2k^2-8b^2}=\dfrac{b^2\left(7k^2+3k\right)}{b^2\left(11k^2-8\right)}=\dfrac{7k^2+3k}{11k^2-8}\left(1\right)\)
\(\dfrac{7c^2+3cd}{11c^2-8d^2}=\dfrac{7d^2k^2+3d^2k}{11d^2k^2-8d^2}=\dfrac{d^2\left(7k^2+3k\right)}{d^2\left(11k^2-8\right)}=\dfrac{7k^2+3k}{11k^2-8}\left(2\right)\)
\(\left(1\right)\left(2\right)\RightarrowĐpcm\)
Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\Rightarrow a=bk,c=dk\)
a) \(\dfrac{a^2-b^2}{c^2-d^2}=\dfrac{b^2k^2-b^2}{d^2k^2-d^2}=\dfrac{b^2}{d^2}\)\(=\dfrac{\dfrac{a}{k}.b}{\dfrac{c}{k}.d}=\dfrac{ab}{cd}=VT\)
Vậy...
b) \(\dfrac{5a+3b}{5a-3b}=\dfrac{5bk+3b}{5bk-3b}=\dfrac{5k+3}{5k-3}\)
\(\dfrac{5c+3d}{5c-3d}=\dfrac{5dk+3d}{5dk-3d}=\dfrac{5k+3}{5k-3}\)
Suy ra \(\dfrac{5a+3b}{5a-3b}=\dfrac{5c+3d}{5c-3d}\)
c) \(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7\left(bk\right)^2+3\left(bk\right).b}{11\left(bk\right)^2-8b^2}\)\(=\dfrac{7k^2+3k}{11k^2-8}\)
\(\dfrac{7c^2+3cd}{11c^2-8d^2}=\dfrac{7\left(dk\right)^2+3\left(dk\right).d}{11\left(dk\right)^2-8d^2}=\dfrac{7k^2+3k}{11k^2-8}\)
Suy ra \(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7c^2+3cd}{11c^2-8d^2}\)
a) Có: \(\dfrac{a}{b}=\dfrac{c}{d}\)
=> \(ad=bc\)
=> \(\dfrac{a}{c}=\dfrac{b}{d}\) => \(\left(\dfrac{a}{c}\right)^2=\left(\dfrac{b}{d}\right)^2=\dfrac{ab}{cd}=\dfrac{a^2}{c^2}=\dfrac{b^2}{d^2}=\dfrac{a^2-b^2}{c^2-d^2}\)
(theo tính chất dãy tỉ số bằng nhau)
=> (đpcm)
b) Có: \(\dfrac{a}{b}=\dfrac{c}{d}\) => \(\dfrac{a}{c}=\dfrac{b}{d}\)
=> \(\dfrac{5a}{5c}=\dfrac{3b}{3d}=\dfrac{5a+3b}{5c+3d}=\dfrac{5a-3b}{5c-3d}\)(theo tính chất dãy tỉ số bằng nhau)
=> \(\dfrac{5a+3b}{5a-3b}=\dfrac{5c+3d}{5c-3d}\) (đpcm)
c) Có: \(\dfrac{a}{b}=\dfrac{c}{d}\Leftrightarrow\dfrac{a}{c}=\dfrac{b}{d}\)
=> \(\dfrac{a^2}{c^2}=\dfrac{ab}{cd}=\dfrac{b^2}{d^2}\) => \(\dfrac{7a^2}{7c^2}=\dfrac{3ab}{3cd}=\dfrac{11a^2}{11c^2}=\dfrac{8b^2}{8d^2}\)
=> \(\dfrac{7a^2+3ab}{7c^2+3cd}=\dfrac{11a^2-8b^2}{11c^2-8d^2}\) (theo tính chất dãy tỉ số bằng nhau)
=> \(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7c^2+3cd}{11c^2-8d^2}\)(đpcm)
#Ayumu
Đặt a/b=c/d=k
=>a=bk; c=dk
\(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7b^2k^2+3\cdot bk\cdot b}{11\cdot b^2k^2-8b^2}=\dfrac{7b^2k^2+3b^2k}{11b^2k^2-8b^2}=\dfrac{7k^2+3k}{11k^2-8}\)
\(\dfrac{7c^2+3cd}{11c^2-8d^2}=\dfrac{7d^2k^2+3\cdot dk\cdot d}{11d^2k^2-8d^2}=\dfrac{7k^2+3k}{11k^2-8}\)
Do đó: \(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7c^2+3cd}{11c^2-8d^2}\)
a)\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\)
\(\Rightarrow\left(\frac{a}{c}\right)^2=\left(\frac{b}{d}\right)^2=\frac{a^2}{c^2}=\frac{b^2}{d^2}=\frac{a}{c}\cdot\frac{b}{d}=\frac{ab}{cd}\)
\(\Rightarrow\frac{a^2}{c^2}=\frac{b^2}{d^2}=\frac{ab}{cd}=\frac{a^2+b^2}{c^2+d^2}\)(T/C...)
\(\Rightarrow\frac{ab}{cd}=\frac{a^2+b^2}{c^2+d^2}\left(đpcm\right)\)
b)\(\frac{a}{b}=\frac{c}{d}\Rightarrow\left(\frac{a}{b}\right)^2=\left(\frac{c}{d}\right)^2\Rightarrow\frac{a^2}{b^2}=\frac{c^2}{d^2}=\frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd}\)
\(\Rightarrow\frac{a^2}{b^2}=\frac{c^2}{d^2}=\frac{ac}{bd}=\frac{a^2+c^2}{b^2+d^2}\)(T/C...)
\(\Rightarrow\frac{ac}{bd}=\frac{a^2+c^2}{b^2+d^2}\)
c)\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\)
\(\Rightarrow\left(\frac{a}{c}\right)^2=\left(\frac{b}{d}\right)^2=\frac{a^2}{c^2}=\frac{b^2}{d^2}=\frac{ab}{cd}=\frac{7a^2}{7c^2}=\frac{11a^2}{11c^2}=\frac{8b^2}{8d^2}=\frac{3ab}{3cd}\)
\(\Rightarrow\frac{7a^2}{7c^2}=\frac{11a^2}{11c^2}=\frac{8b^2}{8d^2}=\frac{3ab}{3cd}=\frac{7a^2+3ab}{7c^2+3cd}=\frac{11a^2-8b^2}{11c^2-8d^2}\)
\(\Rightarrow\frac{7a^2+3ab}{11a^2-8b^2}=\frac{7c^2+3cd}{11c^2-8d^2}\left(đpcm\right)\)
a; Đặt a/b=c/d=k
=>a=bk; c=dk
\(\dfrac{ab}{cd}=\dfrac{bk\cdot b}{dk\cdot d}=\dfrac{b^2}{d^2}\)
\(\dfrac{a^2+b^2}{c^2+d^2}=\dfrac{b^2k^2+b^2}{d^2k^2+d^2}=\dfrac{b^2}{d^2}\)
Do đó: \(\dfrac{ab}{cd}=\dfrac{a^2+b^2}{c^2+d^2}\)
b: \(\dfrac{ac}{bd}=\dfrac{bk\cdot dk}{bd}=k^2\)
\(\dfrac{a^2+c^2}{b^2+d^2}=\dfrac{b^2k^2+d^2k^2}{b^2+d^2}=k^2\)
Do đó: \(\dfrac{ac}{bd}=\dfrac{a^2+c^2}{b^2+d^2}\)
c: \(\dfrac{7a^2-3ab}{11a^2-8b^2}=\dfrac{7b^2k^2-3\cdot bk\cdot b}{11b^2k^2-8b^2}=\dfrac{b^2\left(7k^2-3k\right)}{b^2\left(11k^2-8\right)}=\dfrac{7k^2-3k}{11k^2-8}\)
\(\dfrac{7c^2-3cd}{11c^2-8d^2}=\dfrac{7d^2k^2-3kd^2}{11d^2k^2-8d^2}=\dfrac{7k^2-3k}{11k^2-8}\)
Do đó: \(\dfrac{7a^2-3ab}{11a^2-8b^2}=\dfrac{7c^2-3cd}{11c^2-8d^2}\)
Cùng thêm vào cả tử số và mẫu số một số đơn vị thì hiệu vẫn không đổi.
Hiệu của tử số và mẫu số là: 92 – 67 = 25
Hiệu số phần bằng nhau: 4 – 3 = 1 (phần)
Tử số của phân số mới là: 25 : 1 x 3 = 75
Số cần thêm vào là; 75 – 67 = 8
ĐS: 8
a)
b)
Ta có: \(\frac{a}{b}=\frac{c}{d}.\)
\(\Rightarrow\left(\frac{a}{b}\right)^2=\left(\frac{c}{d}\right)^2=\frac{a}{b}.\frac{c}{d}\)
\(\Rightarrow\left(\frac{a}{b}\right)^2=\left(\frac{c}{d}\right)^2=\frac{ac}{bd}.\)
\(\Rightarrow\frac{a^2}{b^2}=\frac{c^2}{d^2}=\frac{ac}{bd}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được:
\(\frac{a^2}{b^2}=\frac{c^2}{d^2}=\frac{ac}{bd}=\frac{a^2+c^2}{b^2+d^2}.\)
\(\Rightarrow\frac{ac}{bd}=\frac{a^2+c^2}{b^2+d^2}\left(đpcm\right).\)
Chúc bạn học tốt!
Đây là gì :![](data:image/png;base64,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)