Tìm x , biết a) ( x -1 ) mũ 4 + ( x - 2 ) mũ 4 = 1
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a. x mũ 2 - 2x + 1 = 25
= x^2 + 2.x.1 + 1^2
= ( x + 1 ) ^2
ko bt có đúng ko nữa, mấy câu kia tui ko bt lm
b: Ta có: \(2^{x+3}+2^x=144\)
\(\Leftrightarrow2^x\cdot9=144\)
\(\Leftrightarrow2^x=16\)
hay x=4
a, ( 2x - 3 )2- (2x + 1)2 = -3
4x2-12x+9-4x2+4x-1=-3
-8x-1=-3
-8x=-2
x=\(\frac{1}{4}\)
b, (5x - 1) 2 - (5x + 4)(5x - 4) = 7
25x2-10x+1-25x2+16=7
-10x+17=7
-10x=-10
x=1
c, ( x- 5)2 + (x-3)(x+3) - 2(x + 1)2=0
x2-10x+25+x2-9-2x2-4x-2=0
-14x+14=0
-14(x-1)=0
=>x-1=0
x=1
a) \(\left(2x-3\right)^2-\left(2x+1\right)^2=-3\)
\(\Leftrightarrow4x^2-12x+9-4x^2-4x-1=-3\)
\(\Leftrightarrow-16x+8=-3\)
\(\Leftrightarrow-16x=-11\)
\(\Leftrightarrow x=\frac{11}{16}\)
b)\(\left(5x-1\right)^2-\left(5x+4\right)\left(5x-4\right)=7\)
\(\Leftrightarrow25x^2-10x+1-25x^2+16=7\)
\(\Leftrightarrow-10x+17=7\)
\(\Leftrightarrow-10x=-10\)
\(\Leftrightarrow x=1\)
c)\(\left(x-5\right)^2+\left(x-3\right)\left(x+3\right)-2\left(x+1\right)^2=0\)
\(\Leftrightarrow x^2-10x+25+x^2-9-2\left(x^2+2x+1\right)=0\)
\(\Leftrightarrow2x^2-10x-16-2x^2-4x-2=0\)
\(\Leftrightarrow-14x-18=0\)
\(\Leftrightarrow-14x=18\)
\(\Leftrightarrow x=-\frac{9}{7}\)
#H
M = 40 + 41 + 42 + 43 + ... + 498
=> 4M = 41 + 42 + 43 + 44 + ... + 499
Khi đó 4M - M = (41 + 42 + 43 + 44 + ... + 499) - (40 + 41 + 42 + 43 + ... + 498)
=> 3M = 499 - 40 = 499 - 1
Khi đó 2x = 3M + 1
<=> 2x = 499 - 1 + 1
=> 2x = 499
=> 2x = (22)99
=> 2x = 22.99
=> 2x = 2198
=> x = 198
Vậy x = 198
M = 40 + 41 + 42 + 43 + ... + 498
4M = 4( 40 + 41 + 42 + 43 + ... + 498 )
= 41 + 42 + 43 + 44 + ... + 499
=> 3M = 4M - M
= 41 + 42 + 43 + 44 + ... + 499 - ( 40 + 41 + 42 + 43 + ... + 498 )
= 41 + 42 + 43 + 44 + ... + 499 - 40 - 41 - 42 - 43 - ... - 498
= 499 - 1
2x = 3M + 1
<=> 2x = 499 - 1 + 1
<=> 2x = 499
<=> 2x = (22)99 = 2198
<=> x = 198
a) 3/4 + 1/4: x = -3
1/4: x = -3 - 3/4
1/4 : x = -15/4
x = 1/4 : -15/4
x = -1/15
Bài 3
a) x^3 = x^5 => x^5 - x^3 =0 => x^3( x^2 - 1 ) = 0
=> x^3(x - 1 ) ( x+ 1 )= 0
=> x^3 = 0 hoặc x - 1 = 0 hoặc x + 1 = 0
=> x = 0 hoặc x = 1 hoặc x -1
tick đúng cho mình nha
a)100-7.[x-5]=58
7.[x-5]=100-58=42
x-5=42:7=6
x=6+5
x=11
b)12.[x-1]:3=43+23
12 [x-1]:3=64+8
12.[x-1]:3=72
[x-1]:3=72:12=6
[x-1]=6.3=18
x=18-1
x=17
tao koooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo biếtttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
1a.4,9,16,25,36,49,64,91,110,121,144,169,400,900,1600
b. 8,27,64,125,1000
C1111^2=1234321
2. x=6 ,x=3,x=0, x k thuộc n, x k thuộc n
Đặt \(a=x-1\Rightarrow x-2=a-1\)
Ta có :
\(a^4+\left(a-1\right)^4=1\)
\(\Leftrightarrow a^4+a^4-4a^3+6a^2-4a+1=1\)
\(\Leftrightarrow2a^4-4a^3+6a^2-4a=0\)
\(\Leftrightarrow a\left(2a^3-4a^2+6a-4\right)=0\)
\(\Leftrightarrow a\left(2a^3-2a^2-2a^2+2a+4a-4\right)=0\)
\(\Leftrightarrow a\left[2a^2\left(a-1\right)-2a\left(a-1\right)+4\left(a-1\right)\right]=0\)
\(\Leftrightarrow a\left(a-1\right)\left(2a^2-2a+4\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}a=0\\a=1\\2a^2-2a+4=2\left(a-\frac{1}{2}\right)^2+\frac{7}{2}=0\left(l\right)\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\x-1=1\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=2\end{cases}}}\)
Chúc bạn học tốt !!!