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P(x) + Q(x)= ( x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x) + ( 5x^4 - x^5 + 4x^2 - 2x^3 - 1/4)
= x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x + 5x^4 - x^5 + 4x^2 - 2x^3 - 1/4
= ( x^5 - x^5 ) - ( 2x^2 + 4x^2) + ( 7x^4 + 5x^4) - ( 9x^3 - 2x^3) - 1/4x - 1/4
= 6x^2 + 12x^4 - 6x^3 - 1/4x - 1/4
P(x) - Q(x)= ( x^5 - 2x^2 + 7x^4 - 9x^3 -1/4x) - ( 5x^4 - x^5 + 4x^2 - 2x^3 -1/4)
= x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x - 5x^4 + x^5 - 4x^2 + 2x^3 + 1/4
= ( x^5 + x^5) - ( 2x^2 - 4x^2) + ( 7x^4 - 5x^4) - ( 9x^3 + 2x^3) - 1/4x + 1/4
= 2x^5 - (-2)x^2 + 2x^4 - 11x^3 - 1/4x + 1/4
P(x)=x^5+ 7x^4- 9x^3+ 2x^2-1/4x-0
Q(x)=(-x^5+5x^4- 2x^3+ 4x^2+0x-1/4
= 12x^4-11x^3+ 6x^2-1/4x-1/4
P(x) = x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x
=x5+7x4-9x3-2x2-1/4x
Q(x) = 5x^4 - x^5 + 4x^2 - 2x^3 - 1/4
=-x5+5x4-2x3+4x2-1/4
P(x)+Q(x)=x5+7x4-9x3-2x2-1/4x -x5+5x4-2x3+4x2-1/4
=x5-x5+7x4+5x4-9x3-2x3-2x2+4x2-1/4x-1/4
=12x4-11x3+2x2-1/4x-1/4
P(x)-Q(x)=x5+7x4-9x3-2x2-1/4x +x5-5x4+2x3-4x2+1/4
=x5+x5+7x4-5x4-9x3+2x3-2x2-4x2-1/4x-1/4
=2x5+2x4-7x3-6x2-1/4x-1/4
a: \(4x^3+12=120\)
=>\(4x^3=108\)
=>\(x^3=27=3^3\)
=>x=3
b: \(\left(x-4\right)^2=64\)
=>\(\left[{}\begin{matrix}x-4=8\\x-4=-8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=12\\x=-4\end{matrix}\right.\)
c: (x+1)^3-2=5^2
=>\(\left(x+1\right)^3=25+2=27\)
=>x+1=3
=>x=2
d: 136-(x+5)^2=100
=>(x+5)^2=36
=>\(\left[{}\begin{matrix}x+5=6\\x+5=-6\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-11\end{matrix}\right.\)
e: \(4^x=16\)
=>\(4^x=4^2\)
=>x=2
f: \(7^x\cdot3-147=0\)
=>\(3\cdot7^x=147\)
=>\(7^x=49\)
=>x=2
g: \(2^{x+3}-15=17\)
=>\(2^{x+3}=32\)
=>x+3=5
=>x=2
h: \(5^{2x-4}\cdot4=10^2\)
=>\(5^{2x-4}=\dfrac{100}{4}=25\)
=>2x-4=2
=>2x=6
=>x=3
i: (32-4x)(7-x)=0
=>(4x-32)(x-7)=0
=>4(x-8)*(x-7)=0
=>(x-8)(x-7)=0
=>\(\left[{}\begin{matrix}x-8=0\\x-7=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=8\\x=7\end{matrix}\right.\)
k: (8-x)(10-2x)=0
=>(x-8)(x-5)=0
=>\(\left[{}\begin{matrix}x-8=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=5\end{matrix}\right.\)
m: \(3^x+3^{x+1}=108\)
=>\(3^x+3^x\cdot3=108\)
=>\(4\cdot3^x=108\)
=>\(3^x=27\)
=>x=3
n: \(5^{x+2}+5^{x+1}=750\)
=>\(5^x\cdot25+5^x\cdot5=750\)
=>\(5^x\cdot30=750\)
=>\(5^x=25\)
=>x=2
1) 2(3x + 5) - 6 = 0
2(3x + 5) = 6 + 0
2(3x + 5) = 6
3x + 5 = 6 : 2
3x + 5 = 3
3x = 5 - 3
3x = 2
x = 2 : 3
x = 2/3
2) 5x + 3(4 + 2x) = 25
11x + 12 = 25
11x = 25 - 12
11x = 13
x = 13 : 11
x = 13/11
3) 3(4x + 1) + 2(x - 1) = 105
14x + 1 = 105
14x = 105 - 1
14x = 104
x = 104 : 14
x = 104/14 = 52/7
4) 30 - [2(x - 3) - 2] = 14
[2(x - 3) - 2] = 30 - 14
[2(x - 3) - 2] = 16
2x - 8 = 16
2x = 16 + 8
2x = 24
x = 24 : 2
x = 12
5) 3(x - 8)(4x + 5) - 8(x - 8) = 0
12x2 - 89x - 56 = 0
x = 8 hoặc -7/12
6) 4x = 8
Vì: 41 = 4
42 = 16
=> x thuộc tập hợp rỗng
Lời giải:
1. $(x+2)-2=0$
$x+2=2$
$x=0$
2.
$(x+3)+1=7$
$x+3=7-1=6$
$x=6-3=3$
3.
$(3x-4)+4=12$
$3x-4+4=12$
$3x=12$
$x=12:3=4$
4.
$(5x+4)-1=13$
$5x+4=13+1=14$
$5x=14-4=10$
$x=10:5=2$
5.
$(4x-8)-3=5$
$4x-8=5+3=8$
$4x=8+8=16$
$x=16:4=4$
6.
$3+(x-5)=7$
$x-5=7-3=4$
$x=4+5=9$
7.
$8-(2x-4)=2$
$2x-4=8-2=6$
$2x=6+4=10$
$x=10:2=5$
8.
$7+(5x+2)=14$
$5x+2=14-7=7$
$5x=7-2=5$
$x=5:5=1$
9.
$5-(3x-11)=1$
$3x-11=5-1=4$
$3x=11+4=15$
$x=15:3=5$
10.
$16-(8x+2)=6$
$8x+2=16-6=10$
$8x=10-2=8$
$x=8:8=1$
\(A(x)=(2x-4)(x+1)=0\)
\(\Leftrightarrow\orbr{\begin{cases}2x-4=0\\x+1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2\\x=-1\end{cases}}\)
Vậy đa thức \(A(x)\)có hai nghiệm đó là 2 và -1
\(B(x)=(-5x+2)(x-7)=0\)
\(\Leftrightarrow\orbr{\begin{cases}-5x+2=0\\x-7=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}-5x=-2\\x=7\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{2}{5}\\x=7\end{cases}}\)
Vậy đa thức \(B(x)\)có hai nghiệm đó là 2/5 và 7
\(C(x)=(4x-3)(2x+3)=0\)
\(\Leftrightarrow\orbr{\begin{cases}4x-3=0\\2x+3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{3}{4}\\x=-\frac{3}{2}\end{cases}}\)
Vậy đa thức \(C(x)\)có hai nghiệm đó là 3/4 và -3/2
1) 2(3x+5)-6=9
2(3x+5) =9+6
2(3x+5) =15
3x+5 = 15:2
3x+5 = \(\frac{15}{2}\)
3x = \(\frac{15}{2}-5\)
3x =\(\frac{5}{2}\)
x = \(\frac{5}{2}:3\)
x = \(\frac{5}{6}\)
2) 5x+3(4+2x)=25
5x+12+6x=25
5x+6x =-12+25
11x =13
x =13:11
x =\(\frac{13}{11}\)
3) 3(4x+1)+2(x-1)=105
12x+3+2x-2=105
12x+2x = -3+2+105
14x =104
x = 104:14
x = \(\frac{52}{7}\)
4) \(30-[2\left(x-3\right)-2]=14\)
\(2\left(x-3\right)-2\)=\(30-14\)
\(2\left(x-3\right)-2=16\)
\(2\left(x-3\right)=16+2\)
\(2\left(x-3\right)=18\)
\(x-3=18:2\)
\(x-3=9\)
\(x=9+3\)
\(x=12\)
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