Question

Cho a/b=c/d

C/m 2a^2-3ab+5b^2/2b^2+3ab=2c^2-3cd+5d^2/2d^2+3cd

 Giúp mk nhanh đi. Rồi mình tick cho

 

Answer 1

Ta có : \(\frac{a}{b}=\frac{c}{d}\)=> \(\frac{a}{c}=\frac{b}{d}\)

Đặt \(\frac{a}{c}=\frac{b}{d}=k\)=> \(\hept{\begin{cases}a=ck\\d=dk\end{cases}}\)

Khi đó, ta có : \(\frac{2\left(ck\right)^2-3\left(ck\right)\left(dk\right)+5\left(dk\right)^2}{2\left(dk\right)^2+3\left(ck\right)\left(dk\right)}=\frac{2c^2k^2-3cdk^2+5d^2k^2}{2d^2k^2+3cdk^2}=\frac{\left(2c^2-3cd+5d^2\right)k^2}{\left(2d^2+3cd\right)k^2}\)

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