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\(\frac{86}{\left[2.\left(2x-1\right)^2-7\right]}+4^2=2.3^2\Leftrightarrow\frac{86}{\left[2.\left(2x-1\right)^2-7\right]}=2.9-4^2=2\)
\(\frac{86}{2}=\left[2.\left(2x-1\right)^2-7\right]=2.\left(2x-1\right)^2-7\)
\(43=2.\left(2x-1\right)^2-7\Leftrightarrow2.\left(2x-1\right)^2=43+7=50\)
\(\left(2x-1\right)^2=\frac{50}{2}=25=5^2\Rightarrow!2x-1!=5\)
\(\orbr{\begin{cases}2x-1=-5\\2x-1=5\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=-4\\2x=6\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-2\\x=3\end{cases}}}}\)
86 : [2 . (2x - 1)2 - 7] +42=2.32
86 : [2.(2x-1)2-7] + 16 = 2.9
86 : [2.(2x-1)2-7] +16 = 18
86 : [2.(2x-1)2-7]=18-16
86 : [2.(2x-1)2-7]=2
2.(2x-1)2-7=86:2
2.(2x-1)2-7=43
2.(2x-1)2=43+7
2.(2x-1)2=50
(2x-1)2=50:2
(2x-1)2=25
(2x-1)2=52
=>2x-1=5
2x=5+1
2x=6
x=6:2
x=3
a) \(\left(\left|x\right|+3\right):5-3=12\Leftrightarrow\left|x\right|+3=45\Leftrightarrow\orbr{\begin{cases}x=42\\x=-42\end{cases}}\)
b) \(86:\left[2\left(2x-1\right)^2-7\right]+4^2=2\cdot3^2\Leftrightarrow2\left(2x-1\right)^2-7=43\Leftrightarrow\left(2x-1\right)^2=25\Leftrightarrow\orbr{\begin{cases}2x-1=-5\\2x-1=5\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-2\\x=3\end{cases}}\)
a) \(\left(\left|x\right|+3\right)\div5-3=12\)
\(\left(\left|x\right|+3\right)\div5=12+3\)
\(\left(\left|x\right|+3\right)\div5=15\)
\(\left|x\right|+3=15.5\)
\(\left|x\right|+3=75\)
\(\left|x\right|=75-3\)
\(\left|x\right|=72\)
\(\Rightarrow\orbr{\begin{cases}x=72\\x=-72\end{cases}}\)
Vậy \(x\in\left\{72;-72\right\}\)
b) \(86\div\left[2,\left(2x-1\right)^2-7\right]+4^2=2.3^2\)
\(86\div\left[2.\left(2x-1\right)^2-7\right]+16=18\)
\(86\div\left[2.\left(2x-1\right)^2-7\right]=18-16\)
\(86\div\left[2.\left(2x-1\right)^2-7\right]=2\)
\(2.\left(2x-1\right)^2-7=86\div2\)
\(2.\left(2x-1\right)^2-7=43\)
\(2.\left(2x-1\right)^2=43+7\)
\(2.\left(2x-1\right)^2=50\)
\(\left(2x-1\right)^2=50\div2\)
\(\left(2x-1\right)^2=25\)
\(\left(2x-1\right)^2=5^2\)
\(\Rightarrow2x-1=5\)
\(2x=5+1\)
\(2x=6\)
\(x=6\div2\)
\(x=3\)
Câu 1 Tính
a) \(-54\) + 75 - \(\frac{1}{2}\) - 79 - 42\(\frac{1}{2}\)
= 21 - \(-78,5\)- 42\(\frac{1}{2}\)
= \( 99,5\) - 42\(\frac{1}{2}\)
= 57
Câu 2 Tính nhanh
a) 47 . 134 - 47 . 35 + 47
= 47 . ( 134 - 35 ) + 47
= 47 . 99 + 47
= 4653 + 47
= 4700
Câu 3:
a: =>(|x|+3)*15=75
=>|x|+3=5
=>x=2 hoặc x=-2
b: =>86:[2(2x-1)^2-7]=2*9-16=2
=>2(2x-1)^2-7=43
=>2(2x-1)^2=50
=>(2x-1)^2=25
=>2x-1=5 hoặc 2x-1=-5
=>x=-2 hoặc x=3
Bài làm
a. ( | x | + 3 ) . 15 - 5 = 70
( | x | + 3 ) . 15 = 70 + 5
( | x | + 3 ) . 15 = 75
| x | + 3 = 75 : 15
| x | + 3 = 5
| x | = 5 - 3
suy ra | x | = 2 hoặc | x | = -2
vì |2| = 2 ; |-2| = 2
b.86 : [ 2 . ( 2x - 1 )2 - 7 ] + 42 = 2 . 32
86 : [ 2 . ( 2x - 1 )2 - 7 ] + 16 = 2 . 9
86 : [ 2 . ( 2x - 1 )2 - 7 ] + 16 = 18
86 : [ 2 . ( 2x - 1 )2 - 7 ] = 18 - 16
86 : [ 2 . ( 2x - 1 )2 - 7 ] = 2
[ 2 . ( 2x - 1 )2 - 7 ] = 86 : 2
2 . ( 2x - 1 )2 - 7 = 43
2 . ( 2x - 1 ) 2 = 43 + 7
2 . ( 2x - 1 ) 2 = 50
( 2x - 1 ) 2 = 50 : 2
( 2x - 1 ) 2 = 25
( 2x - 1 ) 2 = 52
suy ra ( 2.3 - 1 ) 2 = 52 = 25
B1:
a, 4(a - 3) - (a2 + 2a) - 5a
= 4a - 12 - a2 - 2a - 5a
= - a2 - 3a - 12
b, a(a+3) - [a(a-3) + 2(a+1)]
= a2 + 3a - [a2 - 3a + 2a + 2]
= a2 + 3a - a2 + 3a - 2a - 2
= 4a - 2
B2:
a, 3(x-4) - (2x+3) = 7-2x
=> 3x - 12 - 2x - 3 = 7 - 2x
=> x - 15 = 7 - 2x
=> 3x = 22
=> x = \(\frac{22}{3}\)
b, x(x2-3) - (x3+x) - 5x = (-8)2
=> x3 - 3x - x3 - x - 5x = 64
=> -9x = 64
=> x = \(\frac{-64}{9}\)
c, x(x-1) - 3(x+2) - x2 = -2.33
=> x2 - x - 3x - 6 - x2 = -54
=> -4x = -48
=> x = 12