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\(a,\left(2y+1\right)^3=125\)
\(\Leftrightarrow2y+1=\sqrt[3]{125}=5\)
\(\Leftrightarrow2y=5-1=4\)
\(\Rightarrow y=2\)
\(b,\left(y-5\right)^4=\left(y-5\right)^6\)
\(\Leftrightarrow\left(y-5\right)^4-\left(y-5\right)^6=0\)
\(\Leftrightarrow\left(y-5\right)^4\left[1-\left(y-5\right)^2\right]=0\)
\(\Leftrightarrow\left(y-5\right)^4\left(1-y+5\right)\left(1+y-5\right)=0\)
\(\Leftrightarrow\left(y-5\right)^4\left(6-y\right)\left(y-4\right)=0\)
Vì \(\left(y-5\right)^4>0\forall y\)
\(\Rightarrow\left[{}\begin{matrix}6-y=0\\y-4=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}y=6\\y=4\end{matrix}\right.\)
a) \(\left(2y+1\right)^3=125\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(2y+1\right)^3=5^3\\\left(2y+1\right)^3=\left(-5\right)^3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2y+1=5\\2y+1=-5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2y=4\\2y=-6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=2\\y=-3\end{matrix}\right.\)
Vậy ...................
toi nay mk se lay y kien cua cac ban , giup mk nha
b1
a) \(\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\)
\(=\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=\dfrac{1}{5}-\dfrac{1}{10}\)
\(=\dfrac{2}{10}-\dfrac{1}{10}\)
\(=\dfrac{1}{10}\)
b) \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\)
\(=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=\dfrac{1}{1}-\dfrac{1}{100}\)
\(=\dfrac{99}{100}\)
c) \(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}\)
\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\)
\(=\dfrac{1}{3}-\dfrac{1}{11}\)
\(=\dfrac{8}{33}\)
d) \(\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\)
\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\)
\(=\dfrac{1}{3}-\dfrac{1}{101}\)
\(=\dfrac{98}{303}\)
A= 3( 1+3+3^2+3^3+3^4+3^5+3^6+3^7+3^8) chia hết cho 3
a) x+30%x=-1.31
=> 100%x+30%x=-1.31
=>x.(100%+30%)=-1.31
=>x.13/10=-1.31=-1.31:13/10=-131/130
b) (x-1/2):1/3+5/7=9+5/7
=>(x-1/2).3+5/7=68/7
=>(x-1/2).3=68/7-5/7=9
=>x-1/2=9:3=3
=>x=3+1/2=3 1/2( hỗn số)
c) 1/2x-3/4=14/9.3/7
=>1/2x-3/4=2/3
=>1/2x=2/3+3/4=17/12
x=17/12:1/2=17/12.2=17/6
d) - 5/6 -x = 7/12+ -1/3
=>- 5/6 -x = 7/12+ -4/12=1/4
=> x = -5/6 -1/4=-13/12
e) x + 3/-15 = 1/3
=> x= 1/3 - -3/15 =1/3+3/15
=> x=5/15 + 3/15=8/15
f) (4,5 -2 x). (-1 4/7)=11/14
=> 4,5 -2x=11/14 : -3/7=11/14. -7/3=-11/6
=>-2x=-11/6-9/2= -11/6 -27/6 =-19/3
=>x= -19/3: -2x=19/6
Chúc bn thi HKII tốt!!!
13 - 12 + 11 + 10 - 9 + 8 - 7 -6+ 5 -4 + 3 + 2 -1
= 13 - ( 12 - 11 - 10 + 9 ) + ( 8-7-6+ 5 ) - ( 4 - 3 - 2 + 1 )
= 13 - 0 + 0 -0
=13
Học tốt !
Đặt \(A=5+5^2+5^3+....+5^{199}+5^{200}\)
\(\Leftrightarrow5A=5\left(5+5^2+5^3+....+5^{199}+5^{200}\right)\)
\(\Leftrightarrow5A=5^2+5^3+5^4+....+5^{200}+5^{201}\)
\(\Leftrightarrow5A-A=\left(5^2+5^3+5^4+....+5^{200}+5^{201}\right)-\left(5+5^2+5^3+....+5^{199}+5^{200}\right)\)
\(\Leftrightarrow4A=5^{201}-5\)
\(\Leftrightarrow A=\frac{5^{201}-5}{4}\)