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#)Giải :
a)\(2009^{\left(1000-1^3\right)\left(1000-2^3\right)...\left(1000-15^3\right)}=2009^{\left(1000-1^3\right)...\left(1000-10^3\right)...\left(1000-15^3\right)}=2009^0=1\)
b)\(\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)=\left(\frac{1}{125}-\frac{1}{1^3}\right)...\left(\frac{1}{125}-\frac{1}{5^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)=\left(\frac{1}{125}-\frac{1}{1^3}\right)...0...\left(\frac{1}{125}-\frac{1}{25^3}\right)=0\)
\(A=\)\(\left(1^3-1000\right).\left(2^3-1000\right)\)\(.....\left(2018^3-1000\right)\)
\(A=\left(1^3-1000\right).\left(2^3-1000\right)...\left(10^3-1000\right)...\left(2018^3-1000\right)\)
\(A=\left(1^3-1000\right).\left(2^3-1000\right)...0...\left(2018^3-1000\right)\)
\(A=0\)
~~~Hok tốt~~~
Trong biểu thức trên có chứa (1000-103), mà (1000-103)=1000-1000=0
Do đó tích trên bằng 0
\(\left(1000-1^3\right)\left(1000-2^3\right)\left(1000-3^3\right)...\left(1000-10^3\right)...\left(1000-50^3\right)\)
\(=\left(1000-1^3\right)\left(1000-2^3\right)\left(1000-3^3\right)...\left(1000-1000\right)...\left(1000-50^3\right)\)
\(=\left(1000-1^3\right)\left(1000-2^3\right)\left(1000-3^3\right)...\cdot0\cdot\left(1000-50^3\right)\)
\(=0\)
\(\left(\frac{1}{38}-1\right).\left(\frac{1}{37}-1\right).\left(\frac{1}{36}-1\right)....\left(\frac{1}{2}-1\right)\)
\(=-\left(1-\frac{1}{38}\right).\left(1-\frac{1}{37}\right)....\left(1-\frac{1}{2}\right)\)
\(=-\frac{37}{38}.\frac{36}{37}...\frac{1}{2}\)
\(=\frac{-1}{38}\)
\(\left(\frac{1}{38}-1\right)\left(\frac{1}{37}-1\right)\left(\frac{1}{36}-1\right).......\left(\frac{1}{2}-1\right)\)
\(=\frac{-37}{38}.\frac{-36}{37}.\frac{-35}{36}.......\frac{-2}{3}.\frac{-1}{2}\)
\(=\frac{-1}{38}\)
\(=2^{\left(100-1^2\right)\left(100-2^2\right)...\left(100-10^2\right)...\left(100-15^2\right)}\)
=20=1
1, x2 = 0
=> x=0
2,x2=1
=> x= 1 hoặc x=-1
3,x2=3
=>\(x=\sqrt{3}\)
4,x2=6
=>\(x=\sqrt{6}\)
5,x2=7
=>\(x=\sqrt{7}\)
Ta thấy trong tích có thừa số ( 216 - 6\(^3\)) = 216 - 216 = 0 nên tích bằng 0
Vậy M = 0 + ( 216 x 64 + 216 x 36 )
M = 216 . ( 64 + 36 )
M = 216 x 100
M = 21600
\(2009^{\left(1000-1^3\right).\left(1000-2^3\right)...\left(1000-15^3\right)}\)
= \(2009^{\left(1000-1^3\right).\left(1000-2^3\right)...\left(1000-10^3\right)..\left(1000-15^3\right)}\)
= \(2009^{\left(1000-1^3\right).\left(1000-2^3\right)...\left(1000-1000\right)..\left(1000-15^3\right)}\)
= \(2009^{\left(1000-1^3\right).\left(1000-2^3\right)...0..\left(1000-15^3\right)}\)
= \(2009^0\)
= \(1\)