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25 tháng 9 2017

         \(\frac{31}{2}\)\(.\)\(\frac{32}{2}\)\(.\)\(\frac{33}{2}\)\(....\)\(\frac{60}{2}\)

\(=\)\(\left[\left(31.32.33....60\right)\right]\)\(.\)\(\left(\frac{1.2.3....30}{2^{30}}\right)\)\(.\)\(\left(1.2.3....30\right)\)

\(=\)\(\left[\frac{\left(1.3.5....59\right).\left(2.4.6....60\right)}{2.4.6....60}\right]\)\(=\)\(1.3.5....59\)

Vậy \(\frac{31}{2}\)\(.\)\(\frac{32}{2}\)\(.\)\(\frac{33}{2}\)\(....\)\(\frac{60}{2}\)\(=\)\(1.3.5....59\)

25 tháng 9 2017

ta có:Đặt A= \(1.3.5.....59=\frac{1.2.3.4.....59.60}{2.4.6.....60}\)

=\(\frac{1.2.3.....59.60}{2^{30}.\left(1.2.3.....30\right)}=\frac{31.32.....59.60}{2^{30}}\)

\(\frac{31}{2}.\frac{32}{2}.....\frac{59}{2}.\frac{60}{2}\)

vì \(\frac{31}{2}.\frac{32}{2}.....\frac{59}{2}.\frac{60}{2}\) = \(\frac{31}{2}.\frac{32}{2}.....\frac{59}{2}.\frac{60}{2}\)    

\(\Rightarrow\)A= \(\frac{31}{2}.\frac{32}{2}.....\frac{59}{2}.\frac{60}{2}\)

                                          ( Điều phải chứng minh)

toán nâng cao lớp 6 đấy bạn nha

13 tháng 9 2019

1) \(\left|x-2\right|+2=x\)

\(\Leftrightarrow\left|x-2\right|=x-2\)

\(\Leftrightarrow x-2\ge0\Leftrightarrow x\ge2\)

2) \(x^2+5x+4=0\)

\(\Leftrightarrow x^2+4x+x+4=0\)

\(\Leftrightarrow x\left(x+4\right)+\left(x+4\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(x+4\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+1=0\\x+4=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=-4\end{cases}}\)

3) \(8\sqrt{x}=x^2\)

Bình phương hai vế, ta được: \(64x=x^4\)

\(\Leftrightarrow x^4-64x=0\)

\(\Leftrightarrow x\left(x^3-64\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x^3-64=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=4\end{cases}}\)

13 tháng 9 2019

4) \(\frac{x+29}{31}-\frac{x+27}{33}=\frac{x+17}{43}-\frac{x+15}{45}\)

\(\Leftrightarrow\frac{x+29}{31}-\frac{x+27}{33}-\frac{x+17}{43}+\frac{x+15}{45}=0\)

\(\Leftrightarrow\frac{x+29}{31}+1-\frac{x+27}{33}-1-\frac{x+17}{43}-1+\frac{x+15}{45}+1=0\)

\(\Leftrightarrow\frac{x+60}{31}+\frac{x+60}{45}-\frac{x+60}{33}-\frac{x+60}{43}=0\)

\(\Leftrightarrow\left(x+60\right)\left(\frac{1}{31}+\frac{1}{45}-\frac{1}{33}-\frac{1}{43}\right)=0\)

\(\Leftrightarrow x+60=0\Leftrightarrow x=-60\)

5)\(\left|x-1\right|+3x=1\)

\(\Leftrightarrow\left|x-1\right|=1-3x\)(1)

* Nếu \(x\ge1\)thì \(\left(1\right)\Leftrightarrow x-1=1-3x\Leftrightarrow4x=2\Leftrightarrow x=\frac{1}{2}\left(L\right)\)

* Nếu \(x< 1\)thì \(\left(1\right)\Leftrightarrow1-x=1-3x\Leftrightarrow2x=0\Leftrightarrow x=0\left(TM\right)\)

Vậy x = 0

a) \(\frac{x}{-15}=\frac{-60}{x}\)

\(\Rightarrow x^2=900\)

\(\Rightarrow x=30\)