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c: \(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{7}\\x=-\sqrt{7}\\x=-5\\x=5\end{matrix}\right.\)
\(25\cdot x^2=25\\ x^2=25\div25\\ x^2=1\\ x^2=1^2\\ x=1\\ 8^{x-3}=1\\ 8^{x-3}=8^0\\ x-3=0\\ x=0+3\\ x=3\)
`@` `\text {Ans}`
`\downarrow`
\(3^{x+6}=37\)
`=>`\(3^x\cdot3^6=37\)
`=>`\(3^x=37\div3^6\)
`=>` \(3^x=\dfrac{37}{729}\)
Bạn xem lại đề.
\(25x^2=25\)
`=>`\(x^2=25\div25\)
`=>`\(x^2=1\)
`=> x=1`
\(8^{x-3}=1\)
`=>`\(8^x\div8^3=1\)
`=>`\(8^x=8^3\)
`=> x=3`
`x^2=3`
`=>x=\sqrt{3}\or\x=-\sqrt{3}`
`x^2=36`
`<=>x^2=(+-6)^2`
`<=>x=+-6`
`x^2=25`
`<=>x^2=(+-5)^2`
`<=>x=+-5`
`2x^2+(-20)=55`
`<=>2x^2-20=55`
`<=>2x^2=75`
`<=>x^2=75/2`
`<=>x=+-\sqrt{75/2}`
`2(x-1)^2+5^0=9`
`<=>2(x-1)^2+1=9`
`<=>2(x-1)^2=8`
`<=>(x-1)^2=4`
`<=>x-1=2\or\x-1=-2`
`<=>x=3\or\x=-1`
A=\(\left(1-\frac{1}{2010}\right).\left(1-\frac{2}{2010}\right)...\left(1-\frac{2010}{2010}\right)\left(1-\frac{2011}{2010}\right)\)
A=\(\frac{2009}{2010}.\frac{2008}{2010}...0.\frac{-1}{2010}\)
A=0
a) Ta có: x 2 = 2 2 nên x = 2.
b) Ta có: x 2 = 5 2 nên x = 5.
c) Ta có: 3 x 5 = 3 nên x 5 = 1 . Do đó x = 1.
d) Ta có: 6 x 3 = 48 nên x 3 = 8 . Do đó x = 2.
e) Ta có: x - 1 2 = 2 2 nên x - 1 = 2 . Do đó x = 3.
f) Ta có: x + 1 2 = 5 2 nên x +1 = 5. Do đó x = 4.
g) Ta có: x - 1 3 = 3 3 nên x - 1 = 3 . Do đó x = 4.
h) Ta có: x + 1 3 = 4 3 nên x +1 = 4. Do đó x = 3
Ta có:
a)\(25< 2^x< 3125\)
\(\Rightarrow2^4< 2^x< 2^{12}\)
\(\Rightarrow4< x< 12\)
b)\(\left(x+1\right)+\left(x+2\right)+...+\left(x+100\right)=7450\)
\(\Rightarrow100x+5050=7450\Rightarrow10x=2400\Rightarrow x=240\)
c)\(1+2+3+..+x=\frac{x\left(x+1\right)}{2}=78.\)
\(\Rightarrow x\left(x+1\right)=156\)\(\Rightarrow x=12\)
d)\(12x+13x=25x=2000\Rightarrow x=80\)
e)\(6x+4x=10x=2010\Rightarrow x=201\)
1) \(A=\frac{7}{10\times11}+\frac{7}{11\times12}+\frac{7}{12\times13}+...+\frac{7}{69\times70}\)
\(A=7\times\left(\frac{1}{10\times11}+\frac{1}{11\times12}+\frac{1}{12\times13}+...+\frac{1}{69\times70}\right)\)
\(A=7\times\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{69}-\frac{1}{70}\right)\)
\(A=7\times\left(\frac{1}{10}-\frac{1}{70}\right)\)
\(A=7\times\frac{3}{35}\)
\(A=\frac{3}{5}\)
2) \(B=\frac{1}{25\times27}+\frac{1}{27\times29}+\frac{1}{29\times31}+...+\frac{1}{73\times75}\)
\(B=\frac{1}{2}\times\left(\frac{2}{25\times27}+\frac{2}{27\times29}+\frac{2}{29\times31}+...+\frac{2}{73\times75}\right)\).
\(B=\frac{1}{2}\times\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(B=\frac{1}{2}\times\left(\frac{1}{25}-\frac{1}{75}\right)\)
\(B=\frac{1}{2}\times\frac{2}{75}\)
\(B=\frac{1}{75}\)
3) \(C=\frac{4}{2\times4}+\frac{4}{4\times6}+\frac{4}{6\times8}+...+\frac{4}{2008\times2010}\)
\(C=\frac{4}{2}\times\left(\frac{2}{2\times4}+\frac{2}{4\times6}+\frac{2}{6\times8}+...+\frac{2}{2008\times2010}\right)\)
\(C=2\times\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(C=2\times\left(\frac{1}{2}-\frac{1}{2010}\right)\)
\(C=2\times\frac{502}{1005}\)
\(C=\frac{1004}{1005}\)
_Chúc bạn học tốt_
1. |x|=2011
<=>\(\orbr{\begin{cases}x=2011\\x=-2011\end{cases}}\)
2.1 + x = -2011
x= -2011-1
x= -2012
3. 1 - (-x+2010)=2011
-x+2010=1 - 2011
-x+ 2010= -2010
-x = -2010-2010
-x = -4020
=> x = -4020
4. x2 = 25
x= 25 :2
x=12,5
1) x = 2011 hoặc x = (- 2011)
2) x = (- 2011) -1
x = - 2012
3) x + 2010 = - 2010
x = (- 2010) - 2010
x = - 4020
4) x .2 = 25
x = 25 : 2
x =12,5
Chúc bạn học tốt.