Question

1/ Tìm x, y biết:

   a/ x.3 = y.7 và 2x - y = 4

   b/ Ix - 1I - \(\frac{1}{2}=\frac{3}{4}\) 

   c/ I x + 1 I + I y - 2 I = 0

   d/ (2² :4) . 2^x = 4

2/ Tìm GTNN của:

   a/ A = 3. I2x + 1I +5

   b/ B = I x - 2014I + I x - 2015I

3/ Cho \(\frac{a}{b}=\frac{c}{d}\) CMR:

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

Answer 1

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

                                       \(\Rightarrow c=d.k\)      

\(-Tacó:\frac{2a-3b}{2a+3b}=\frac{2k.b-3b}{2k.b+3b}=\frac{b.\left(2k-3\right)}{b\left(2k+3\right)}=\frac{2k-3}{2k+3}\left(1\right)\)

\(-Tacó:\frac{2c-3d}{2c+3d}=\frac{2d.k-3d}{2d.k+3d}=\frac{d.\left(2k-3\right)}{d.\left(2k+3\right)}=\frac{2k-3}{2k+3}\left(2\right)\)

\(Từ\left(1\right),\left(2\right)\Rightarrow\frac{2a-3b}{2a+3b}=\frac{2c-3d}{2c+3d}\)