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bài 1 tính giá trị biểu thức
( - 25 ) nhân ( -3 ) nhân x với x = 4
\(\left(-25\right).\left(-3\right).4\)
\(=\left(-25\right).4.\left(-3\right)\)
\(=-100.\left(-3\right)=300\)
( -1 ) nhân ( -4 ) nhân 5 nhân 8 nhân y với y =25
\(\left(-1\right).\left(-4\right).5.8.25\)
\(=4.5.8.25=4.25.5.8\)
\(=100.40=40000\)
( 2ab mũ 2 ) : c với a =4 ; b= -6 ; c =12
\(\left(2.4.\left(-6\right)\right)^2:12\)
\(=\left(-48\right)^2:12\)
\(=2304:12=192\)
[ ( -25 ) nhân ( - 27 ) nhân ( -x ) ] : y với x = 4 ; y = -9
\(\left[\left(-25\right).\left(-27\right).\left(-4\right)\right]:-9\)
\(=-2700:\left(-9\right)\)
\(=300\)
(a mũ 2 _ b mũ 2) : ( a + b ) nhân ( a _ b ) với a + 5 , b = -3
\(\left(5^2-\left(-3\right)^2\right):\left(5-3\right).\left(5+3\right)\)
\(=16:2.8\)
\(=8.8=64\)
1) \(2^x-15=17\)
\(\Leftrightarrow2^x=32=2^5\)
\(\Rightarrow x=5\)
2) \(\left(7x-11\right)^3=25\cdot5^2+200\)
\(\Leftrightarrow\left(7x-11\right)^3=825\)
\(\Leftrightarrow7x-11=\sqrt[3]{825}\)
\(\Leftrightarrow7x=11+\sqrt[3]{825}\)
\(\Rightarrow x=\frac{11+\sqrt[3]{825}}{7}\)
3) \(\left(x+1\right)^{100}-3\left(x+1\right)^{99}=0\)
\(\Leftrightarrow\left(x+1\right)^{99}\left(x-2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}\left(x+1\right)^{99}=0\\x-2=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-1\\x=2\end{cases}}\)
4) \(4x+5\left(x+3\right)=105\)
\(\Leftrightarrow9x+15=105\)
\(\Leftrightarrow9x=90\)
\(\Rightarrow x=10\)
5) \(5\cdot\left(x-2\right)+10\left(x+3\right)=170\)
\(\Leftrightarrow5\left[x-2+2\left(x+3\right)\right]=170\)
\(\Leftrightarrow3x+4=34\)
\(\Leftrightarrow3x=30\)
\(\Rightarrow x=10\)
\(5.x+x=15:3+13\\ \Rightarrow\left(5+1\right).x=5+13=18\\ \Rightarrow6x=18\\ \Rightarrow x=\dfrac{18}{6}=3\)
\(\dfrac{2}{3}x+\dfrac{1}{3}x+\dfrac{1}{2}=\dfrac{2}{3}\\ \Rightarrow x\left(\dfrac{2}{3}+\dfrac{1}{3}\right)=\dfrac{2}{3}-\dfrac{1}{2}\\ \Rightarrow x=\dfrac{4}{6}-\dfrac{3}{6}=\dfrac{1}{6}\)
\(\dfrac{2}{5}x+x=\dfrac{3}{2}\\ \Rightarrow x\left(\dfrac{2}{5}+1\right)=\dfrac{3}{2}\\ \Rightarrow x\left(\dfrac{2}{5}+\dfrac{5}{5}\right)=\dfrac{3}{2}\\ \Rightarrow x.\dfrac{7}{5}=\dfrac{3}{2}\\ \Rightarrow x=\dfrac{3}{2}:\dfrac{7}{5}\\ \Rightarrow x=\dfrac{3.5}{7.2}=\dfrac{15}{14}\)
\(5\cdot x+x=15:3+13\)
\(\Rightarrow x\cdot\left(5+1\right)=5+13\)
\(\Rightarrow x\cdot6=18\)
\(\Rightarrow x=\dfrac{18}{6}=3\)
================
\(\dfrac{2}{3}\cdot x+\dfrac{1}{3}\cdot x+\dfrac{1}{2}=\dfrac{2}{3}\)
\(\Rightarrow x\cdot\left(\dfrac{2}{3}+\dfrac{1}{3}\right)=\dfrac{2}{3}-\dfrac{1}{2}\)
\(\Rightarrow x\cdot1=\dfrac{1}{6}\)
\(\Rightarrow x=\dfrac{1}{6}\)
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\(\dfrac{2}{5}\cdot x+x=\dfrac{3}{2}\)
\(\Rightarrow x\cdot\left(\dfrac{2}{5}+1\right)=\dfrac{3}{2}\)
\(\Rightarrow x\cdot\dfrac{7}{5}=\dfrac{3}{2}\)
\(\Rightarrow x=\dfrac{3}{2}:\dfrac{7}{5}\)
\(\Rightarrow x=\dfrac{15}{14}\)
a) 0,5 + ( x - 15/2 ) : 1/2 = 9/2
<=> (x - 15/2 ): 1/2 = 9/2 - 0,5
<=> (x - 15/2) : 1/2 = 4
<=> (x - 15/2) = 4 . 1/2
<=> x - 15/2 = 2
<=> x = 2 + 15/2
<=> x = 19/2
b) 2012x - 2010x = 2014
( 2012 - 2010 ) .x = 2014
2x = 2014
x = 2014 :2
x = 1007
2.4^x - 1 = 128
=> 4^x - 1 = 64
=> x - 1 = 3
=> x = 4
b, 17.4^2 + 83.16
= 17.16 + 83.16
= 16(17 + 83)
= 16.100
= 1600
c, a^5 . 10^10.a^15
= a^20.10^10
d, 3{65 - [5(4 + 2.3) - 15] : 7}
= 3{65 - [5(4 + 6) - 15] : 7}
= 3{65 - [5.10 - 15] : 7}
= 3{65 - [50 - 15] : 7}
= 3{65 - 35 : 7}
= 3{65 - 5}
= 3.60
= 180
2^x . 2^x+1 = 2^15
2^x+x+1 = 2^15
x+x+1 = 15
2x + 1 = 15
2x = 15-1
2x = 14
x = 14 : 2
x = 7
2^x.2^x+1=2^15
2^x+x+1=2^15
x+x+1=15
2x+1=15
2x=15-1
2x=14
x=14:2
x=7
Vậy x=7