4x - 15 = -25 - 3x
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Mình làm 5 câu thôi nhé !:
1) \(7^x\cdot49=7^{90}\)
\(\Rightarrow7^x\cdot7^2=7^{90}\)
\(\Rightarrow7^{x+2}=7^{90}\)
\(\Rightarrow x=90-2\)
\(\Rightarrow x=88\)
2) \(2^x\cdot4=128\)
\(\Rightarrow2^x\cdot2^2=2^7\)
\(\Rightarrow2^{x+2}=2^7\)
\(\Rightarrow x=7-2\)
\(\Rightarrow x=5\)
3) \(3^x-1=2^4\cdot5\)
\(\Rightarrow3^x=80+1\)
\(\Rightarrow3^x=81\)
\(\Rightarrow3^x=3^4\)
\(\Rightarrow x=4\)
4) \(3^x+15=42\)
\(\Rightarrow3^x=42-15\)
\(\Rightarrow3^x=27\)
\(\Rightarrow3^x=3^3\)
\(\Rightarrow x=3\)
5) \(4\cdot2^x-3=125\)
\(\Rightarrow2^2\cdot2^x=128\)
\(\Rightarrow2^{x+2}=2^7\)
\(\Rightarrow x=7-2\)
\(\Rightarrow x=5\)
6)
\(5^x=5^{15}:5^3\\ \Leftrightarrow5^x=5^{15-3}\\ \Leftrightarrow5^x=5^{12}\\ \Leftrightarrow x=12\)
7)
\(4^x=4^{15}:16\\ \Leftrightarrow4^x=4^{15}:4^2\\ \Leftrightarrow4^x=4^{15-2}\\ 4^x=4^{13}\\ \Leftrightarrow x=13\)
8)
\(7^x=7^{20}:7^{10}\\ \Leftrightarrow7^x=7^{20-10}\\ \Leftrightarrow7^x=7^{10}\\ \Leftrightarrow x=10\)
9)
\(11^x=11^{11}:11\\ \Leftrightarrow11^x=11^{11-1}\\ \Leftrightarrow11^x=11^{10}\\ \Leftrightarrow x=10\)
10)
\(3^{15}.3^x=3^{30}\\ \Leftrightarrow3^x=3^{30}:3^{15}\\ 3^x=3^{30-15}\\ \Leftrightarrow3^x=3^{15}\\ \Leftrightarrow x=15\)
Bài 1.
1) ( 2x + 1 )3 - ( 2x + 1 )( 4x2 - 2x + 1 ) - 3( 2x - 1 ) = 15
<=> 8x3 + 12x2 + 6x + 1 - [ ( 2x )3 - 13 ] - 6x + 3 = 15
<=> 8x3 + 12x2 + 4 - 8x3 + 1 = 15
<=> 12x2 + 15 = 15
<=> 12x2 = 0
<=> x = 0
2) x( x - 4 )( x + 4 ) - ( x - 5 )( x2 + 5x + 25 ) = 13
<=> x( x2 - 16 ) - ( x3 - 53 ) = 13
<=> x3 - 16x - x3 + 125 = 13
<=> 125 - 16x = 13
<=> 16x = 112
<=> x = 7
Bài 2.
A = ( x + 5 )( x2 - 5x + 25 ) - ( 2x + 1 )3 - 28x3 + 3x( -11x + 5 )
= x3 + 53 - ( 8x3 + 12x2 + 6x + 1 ) - 28x3 - 33x2 + 15x
= -27x3 + 125 - 8x3 - 12x2 - 6x - 1 - 33x2 + 15x
= -33x3 - 45x2 + 9x + 124 ( có phụ thuộc vào biến )
B = ( 3x + 2 )3 - 18x( 3x + 2 ) + ( x - 1 )3 - 28x3 + 3x( x - 1 )
= 27x3 + 54x2 + 36x + 8 - 54x2 - 36x + x3 - 3x2 + 3x - 1 - 28x3 + 3x2 - 3x
= 7 ( đpcm )
C = ( 4x - 1 )( 16x2 + 4x + 1 ) - ( 4x + 1 )3 + 12( 4x + 1 )3 + 12( 4x + 1 ) - 15
= ( 4x )3 - 13 - [ ( 4x + 1 )3 - 12( 4x + 1 )3 - 12( 4x + 1 ) ] - 15
= 64x3 - 1 - ( 4x + 1 )[ ( 4x + 1 )2 - 12( 4x + 1 )2 - 12 ] - 15
= 64x3 - 16 - ( 4x + 1 )[ 16x2 + 8x + 1 - 12( 16x2 + 8x + 1 ) - 12 ]
= 64x3 - 16 - ( 4x + 1 )( 16x2 + 8x - 11 - 192x2 - 96x - 12 )
= 64x3 - 16 - ( 4x + 1 )( -176x2 - 88x - 23 )
= 64x3 - 16 - ( -704x3 - 528x2 - 180x - 23 )
= 64x3 - 16 + 704x3 + 528x2 + 180x + 23
= 768x3 + 528x2 + 180x + 7 ( có phụ thuộc vào biến )
a) \(3x-15=-25-x\)
\(3x+x=-25+15\)
\(4x=-10\)
\(x=\frac{-5}{2}\)
b) \(49-3x=4x+14\)
\(49-14=4x+3x\)
\(35=7x\)
\(x=5\)
a, \(3x-15=-25-x\Leftrightarrow3x-15+25+x=0\Leftrightarrow4x+10=0\)
\(\Leftrightarrow4x=-10\Leftrightarrow x=-\frac{5}{2}\)
b, \(49-3x=4x+14\Leftrightarrow49-3x-4x-14=0\Leftrightarrow35-7x=0\)
\(\Leftrightarrow7x=35\Leftrightarrow x=5\)
+) ta có : \(E=3x^2-6x+15=3\left(x^2-2x+1\right)+12\)
\(=3\left(x-1\right)^2+12\ge12\) \(\Rightarrow E_{min}=12\) khi \(x=1\)
+) ta có : \(F=5x^2+6x-12=5\left(x^2+\dfrac{6}{5}x+\dfrac{9}{25}\right)-\dfrac{69}{5}\)
\(=5\left(x+\dfrac{3}{5}\right)^2-\dfrac{69}{5}\ge\dfrac{-69}{5}\) \(\Rightarrow F_{min}=-\dfrac{69}{5}\) khi \(x=\dfrac{-3}{5}\)
+) ta có : \(G=4x^2-4x+25=4\left(x^2-x+\dfrac{1}{4}\right)+24\)
\(=4\left(x-\dfrac{1}{2}\right)^2+24\ge24\) \(\Rightarrow G_{min}=24\) khi \(x=\dfrac{1}{2}\)
+) ta có : \(H=9x^2+6x^2+4=15x^2+4\ge4\)
\(\Rightarrow H_{min}=4\) khi \(x=0\)
Tìm GTNN
E=3x^2-6x+15
F= 5x^2+6x-12
G=4x^2-4x+25
H=9x^2+6x^2+4
a: =>3x=10+14=24
=>x=8
b: =>25-30-x=-19
=>-5-x=-19
=>x+5=19
=>x=14
c: =>15-x=12+14=26
=>x=-11
d: =>4x+11-x-34=67
=>3x-23=67
=>3x=90
=>x=30
e: =>-x-14=289-36-289=-36
=>x+14=36
=>x=22
a) 3x=24
x=8
b) 25-30-x=-19
25-30+19=x
14=x
c) 15-x=26
x=-11
d) 4x+11-x-34=67
3x=90
x=30
e) -14-x= -36
x=-14 -36
x= 22
=>7x=-10
hay x=-10/7
x=-10/7