đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\Rightarrow a=bk;c=dk\)

Thay a và c vào VP và VT sẽ bằng nhau

Ai help me vs

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

\(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7b^2k^2+3b^2k}{11b^2k^2-8b^2}=\dfrac{b^2\left(7k^2+3k\right)}{b^2\left(11k^2-8\right)}=\dfrac{7k^2+3k}{11k^2-8}\left(1\right)\)

\(\dfrac{7c^2+3cd}{11c^2-8d^2}=\dfrac{7d^2k^2+3d^2k}{11d^2k^2-8d^2}=\dfrac{d^2\left(7k^2+3k\right)}{d^2\left(11k^2-8\right)}=\dfrac{7k^2+3k}{11k^2-8}\left(2\right)\)

\(\left(1\right)\left(2\right)\RightarrowĐpcm\)

Bài 1:

$\frac{a}{b}=\frac{c}{d}=t\Rightarrow a=bt; c=dt$. Khi đó:

\(\frac{2a^2-3ab+5b^2}{2a^2+3ab}=\frac{2(bt)^2-3.bt.b+5b^2}{2(bt)^2+3bt.b}=\frac{b^2(2t^2-3t+5)}{b^2(2t^2+3t)}\)

$=\frac{2t^2-3t+5}{2t^2+3t}(1)$
\(\frac{2c^2-3cd+5d^2}{2c^2+3cd}=\frac{2(dt)^2-3.dt.d+5d^2}{2(dt)^2+3dt.d}=\frac{d^2(2t^2-3t+5)}{d^2(2t^2+3t)}=\frac{2t^2-3t+5}{2t^2+3t}(2)\)

Từ $(1);(2)$ suy ra đpcm.

Bài 2:

Từ $\frac{a}{c}=\frac{c}{b}\Rightarrow c^2=ab$. Khi đó:

$\frac{b^2-c^2}{a^2+c^2}=\frac{b^2-ab}{a^2+ab}=\frac{b(b-a)}{a(a+b)}$ (đpcm)

Bài 3:

Đặt $\frac{a}{b}=\frac{c}{d}=t\Rightarrow a=bt; c=dt$

Khi đó:

$\frac{3a^6+c^6}{3b^6+d^6}=\frac{3(bt)^6+(dt)^6}{3b^6+d^6}=\frac{t^6(3b^6+d^6)}{3b^6+d^6}=t^6(*)$

Và:

$\frac{(a+c)^6}{(b+d)^6}=(\frac{bt+dt}{b+d})^6=t^6(**)$

Từ $(*); (**)\Rightarrow $ đpcm.

\(dat\frac{a}{b}=\frac{c}{d}=k\)->> a=b.k va c=d.k

về phai

\(\frac{7.\left(d.k\right)^2+d.k.d}{11.\left(d.k\right)^2-8.d^2}=\frac{d^2.k\left(7k+1\right)}{d^2.\left(11k^2-8\right)}=\frac{k.\left(7k+1\right)}{11k^2-8}\)

ve trai

\(\frac{7.\left(b.k\right)^2+b.k.b}{11.\left(b.k\right)^2-8b^2}=\frac{b^2k.\left(7k+1\right)}{b^2.\left(11k^2-8\right)}=\frac{k.\left(7k+1\right)}{11k^2-8}\)

vậy vế trái = vế phải --> dpcm ( để bạn ghi có sai cho 3.cd k??_)

k phải toán violympic

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: \(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7c^2+3cd}{11c^2-8d^2}\)

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: \(\dfrac{7a^2+3ab}{11a^2-8b^2}=\dfrac{7c^2+3cd}{11c^2-8d^2}\)

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

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

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

=> bằng nhau

thế thì chúc bạn may mắn

Bằng nhau pạn nhé. Mjk ko tjện giảj nha pạn tự làm nha.