ta cs a/b=c/d=>a/c=b/d

=>2a+3b/2c+3d=3a-4b/3c-4d

=>2a+3b/3a-4b=2c+3d/3c-4d

=>bai toan dc c/m

Cau b tuong tu nha ban

don't forget tick me

a) Ta có \(\frac{a}{b}=\frac{c}{d}.\)

\(\Rightarrow\frac{a}{c}=\frac{b}{d}.\)

Áp dụng tính chất dãy tỉ số bằng nhau ta được:

\(\frac{a}{c}=\frac{b}{d}=\frac{2a}{2c}=\frac{3b}{3d}=\frac{2a+3b}{2c+3d}\) (1).

\(\frac{a}{c}=\frac{b}{d}=\frac{3a}{3c}=\frac{4b}{4d}=\frac{3a-4b}{3c-4d}\) (2).

Từ (1) và (2) \(\Rightarrow\frac{2a+3b}{2c+3d}=\frac{3a-4b}{3c-4d}.\)

\(\Rightarrow\frac{2a+3b}{3a-4b}=\frac{2c+3d}{3c-4d}\left(đpcm\right).\)

Chúc bạn học tốt!

a. Câu hỏi của Nguyễn Ngọc Quế Anh - Toán lớp 7 - Học toán với OnlineMath

mk làm câu a thôi, b dài nhưng tương tự

Gọi a/b=c/d=k =>a=bk ; c=dk

=>\(\frac{\left(2a+3b\right)^2}{\left(3a-4b\right)^2}=\frac{\left(2bk+3b\right)^2}{\left(3bk-4b\right)^2}=\frac{\left[b\left(2k+3\right)\right]^2}{\left[b\left(3k-4\right)\right]^2}=\frac{b^2\left(2k+3\right)^2}{b^2\left(3k-4\right)^2}=\frac{\left(2k+3\right)^2}{\left(3k-4\right)^2}\)(1)

=>\(\frac{\left(2c+3d\right)^2}{\left(3c-4d\right)^2}=\frac{\left(2dk+3d\right)^2}{\left(3dk-4d\right)^2}=\frac{\left[d\left(2k+3\right)\right]^2}{\left[d\left(3k-4\right)\right]^2}=\frac{\left(2k+3\right)^2}{\left(3k-4\right)^2}\)(2)

Từ (1);(2)=> đpcm

Đặt \(\frac{a}{b}=\frac{c}{d}=k=>a=bk,c=dk\)

\(\frac{2a^2-3ab+5b^2}{2b^2+3ab}=\frac{2\left(bk^2\right)-3bkb+5b^2}{2b^2+3bkb}=\frac{2b^2.k^2-3kb^2+5b^2}{2b^2+3b^2.k}\)\(=\frac{b^2\left(2k^2-3k+5\right)}{b^2\left(2+3k\right)}=\frac{2k^2-3k+5}{2+3k}=\frac{2c^2-3cd+5d^2}{2d^2+3cd}\)\(=\frac{2\left(dk\right)^2-3dkd+5d^2}{2d^2+3dkd}=\frac{2d^2k^2-3d^2k+5d^2}{2d^2+3dkd}\)

Tương tự nhóm tiếp là ra

=>bằng nhau

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Đặt a/b=c/d=k rồi thay vào nha bạn

GỢI Ý:

Đặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow a=bk;c=dk\)

Mình hướng dẫn thôi. Chứ giờ đang bận.

Đặt \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow\hept{\begin{cases}a=kb\\c=kd\end{cases}}\).Rồi thay a = kb; c=kd vào từng vế. Thấy hai vế bằng nhau => đpcm

\(\frac{a}{b}=\frac{c}{d}=>\frac{a}{c}=\frac{b}{d}=>\frac{2a^2}{2c^2}=\frac{5b^2}{5d^2}=\frac{3ab}{3ab}=\frac{3cd}{3cd}\)

áp dụng t/c dãy tỉ số bằng nhau ta có:

\(\frac{2a^2}{2c^2}=\frac{5b^2}{5d^2}=\frac{3ab}{3ab}=\frac{3cd}{3cd}=\frac{2a^2-3ab+5b^2}{2b^2-3cd+5d^2}=\frac{2b^2+3ab}{2d^2+3cd}\)

\(=>\frac{2a^2-3ab+5b^2}{2b^2+3ab}=\frac{2c^2-3cd+5d^2}{2d^2+3cd}\)

Đặt\(\frac{a}{b}=\frac{c}{d}=k\),ta có:

\(a=bk\)\(c=dk\)\(\Rightarrow\frac{2a^2-3ab+5b^2}{2b^2+3ab}=\frac{2\left(bk\right)^2-3bkb+5b^2}{2b^2+3bkb}=\frac{2b^2k^2-3b^2k+5b^2}{2b^2+3b^2k}=\frac{b^2.\left(2k^2+3k+5\right)}{b^2.\left(2+3k\right)}\)\(=\frac{2k^2+3k+5}{2+3k}\left(1\right)\)

\(\Rightarrow\frac{2c^2-3cd+5d^2}{2d^2+3cd}=\frac{2\left(dk\right)^2-3dkd+5d^2}{2d^2+3dkd}=\frac{2d^2k^2-3d^2k+5d^2}{2d^2+3d^2k}=\frac{d^2.\left(2k^2+3k+5\right)}{d^2.\left(2+3k\right)}\)

\(=\frac{2k^2+3k+5}{2+3k}\)(2)

Từ (1) và (2) suy ra:

\(\frac{2a^2-3ab+5b^2}{2b^2+3ab}=\frac{2c^2-3cd+5d^2}{2d^2+3cd}\)(đpcm)

\(\frac{a}{b}=\frac{c}{d}\Rightarrow a=bk;c=dk\)

\(\frac{2a^2-3ab+5b^2}{2b^2+3ab}=\frac{2b^2k^2-3b^2k+5b^2}{2b^2+3b^2k}=\frac{b^2\left(2k^2-3k+5\right)}{b^2\left(2+3k\right)}=\frac{2k^2-3k+5}{3k+2}\)

\(\frac{2c^2-3cd+5d^2}{2d^2+3cd}=\frac{2d^2k^2-3d^2k+5d^2}{2d^2+3d^2k}=\frac{d^2\left(2k^2-3k+5\right)}{d^2\left(2+3k\right)}=\frac{2k^2-3k+5}{3k+2}\)

nên 2 phân số trên bằng nhau (đpcm)

Đặt: \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow\hept{\begin{cases}a=bk\\c=dk\end{cases}}\)

Ta có : \(\frac{2a^2-3ab+5b^2}{2b^2+3ab}\)

<=> \(\frac{2b^2k^2-3b^2k+5b^2}{2b^2+3b^2k}\)

<=> \(\frac{b^2\left(2k^2-3k+5\right)}{b^2\left(2+3k\right)}\)

<=> \(\frac{2k^2-3k+5}{2+3k}\left(1\right)\)

Ta có: \(\frac{2c^2-3cd+5d^2}{2d^2+3cd}\)

<=> \(\frac{2d^2k^2-3d^2k+5d^2}{2d^2+3d^2k}\)

<=> \(\frac{d^2\left(2k^2-3k+5\right)}{d^2\left(2+3k\right)}\)

<=> \(\frac{2k^2-3k+5}{2+3k}\left(2\right)\)

Từ 1 và 2 => đpcm