\(x^3+3x-364\)
Giải pt: \(x^3+3x-364=0\)
Bậc 3 ngán lắm:
x(x^2+3)
Phân h con 364 xem
364=4.91=7.4.13.=7.52=7(7^2+3)
ok! x= 7 là nghiệm
\(x^3+3x-364=\left(x-7\right)\left(x^2+7x+52\right)\)
\(\orbr{\begin{cases}x=7\\x^2+7x+\frac{49}{4}=\frac{49}{4}-52< 0\left(VN\right)\end{cases}}\)
x= 7 duy nhất
Hàm bậc 3 (bậc cao) ở mức độ ptth kiểu gì cũng có nghiệm hũu tỷ, các bài nghiệm vô tỷ -->lỗi nhỏ của người ra đề hoặc người chép lại đề cố tình sửa hệ số đi.
Tìm x biết:
a) (2x-4).(3x+12)=0
b) 697:\(\frac{15x+364}{x}\)=17
a, \(\left(2x-4\right)\left(3x+12\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2x-4=0\\3x+12=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}2x=4\\3x=-12\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=2\\x=-4\end{cases}}\)
b, \(697\div\frac{15x+364}{x}=17\)
\(\Rightarrow\frac{15x+364}{x}=697\div17\)
\(\Rightarrow\left(15x+364\right)\div x=41\)
\(\Rightarrow15x+364=41x\)
\(\Rightarrow15x-41x=-364\)
\(\Rightarrow-26x=-364\)
\(\Rightarrow x=-364\div\left(-26\right)\)
\(\Rightarrow x=14\)
tìm x:
a) \(5^{x-2}-3^2=2^4-\left(2^8.2^4-2^{10}.2^2\right)\)
b) 697 : [ ( 15x + 364 ) : x ] = 17
c)\(\left(3x-2^4\right).7^3=2.7^4\)
tìm x:
\(^{5^{x-2}-3^2=2^4-\left(2^8.2^4-2^{10}.2^2\right)}\)
\(697:\left[\left(15x+364\right):x\right]=17\)
\(\left(3x-2^4\right).7^3=2.7^4\)
X×2+X×3+X×4 = 364 - 328
X x 2 + X x 3 + X x 4 = 364 - 328
X x 9 = 36
X = 36 : 9
X = 4
x8+364=0
(x-5)3-x+5=0
5(x-2)-x2+4=0
`x^8+36x^4=0`
`<=>x^4(x^4+36)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x^4=0\\x^4+36=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x^4=-36\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x\in\varnothing\end{matrix}\right.\)
__
`(x-5)^3 -x+5=0`
`<=> (x-5)^3 -(x-5)=0`
`<=> (x-5) [(x-5)^2 -1]=0`
`<=> (x-5)(x-5-1)(x-5+1)=0`
`<=>(x-5)(x-6)(x-4)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x-6=0\\x-4=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=5\\x=6\\x=4\end{matrix}\right.\)
__
`5(x-2)-x^2+4=0`
`<=>5(x-2)-(x^2-4)=0`
`<=>5(x-2)-(x-2)(x+2)=0`
`<=>(x-2)(5-x-2)=0`
`<=>(x-2)(-x-3)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\-x-3=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)
a) 5x - 2 - 32 = 24 - ( 28 . 24 - 210 . 22 )
b) 697 : [( 15x + 364 ) : x ] = 17
c) 134 : ( x - 3 ) = 35 + 160 : 5
d) ( 3x - 24 ) : 73 = 2 . 74
e) [( 10 - x ) : 2 + 5 ] : 3 - 2 = 3
c) 134 : ( x - 3 ) = 35 + 160 : 5
<=> 134 : ( x - 3 ) = 67
<=> x - 3 = 134 : 67
<=> x - 3 = 2
<=> x = 2 + 3
<=> x = 5
c) 134 : ( x - 3 ) = 35 + 160 : 5
134 : ( x - 3 ) = 35 + 32
134 : ( x - 3 ) = 67
( x - 3 ) = 134 : 67
x - 3 = 2
x = 2 + 3
x = 5
1, [(10-x). 2+5 ] : 3-2 = 3
2, 697: [(15x+364):x ] = 17
1/ =>[ (10 - x) . 2 + 5 ] : 3 = 5
=> (10 - x) .2 + 5 = 15
=> (10 - x) . 2 = 10
=> 10 - x = 5
=> x = 5
2/ => (15x + 364) : x = 41
=> 15x + 364 = 41x
=> 26x = 364
=> x = 14
318-5 (x-64)=103
4mũ x . 5 +216=296
376-6 mũ x :3=364
(4x -1) mũ 2=121
\(318-5\left(x-64\right)=103\)
\(\Rightarrow5\left(x-64\right)=318-103\)
\(\Rightarrow5\left(x-64\right)=215\)
\(\Rightarrow x-64=43\)
\(\Rightarrow x=43+64\)
\(\Rightarrow x=107\)
_____________
\(4^x\cdot5+216=296\)
\(\Rightarrow4^x\cdot5=296-216\)
\(\Rightarrow4^x\cdot5-80\)
\(\Rightarrow4^x=16\)
\(\Rightarrow4^x=4^2\)
\(\Rightarrow x=2\)
___________
\(376-6^x:3=364\)
\(\Rightarrow6^x:3=376-364\)
\(\Rightarrow6^x:3=12\)
\(\Rightarrow6^x=36\)
\(\Rightarrow6^x=6^2\)
\(\Rightarrow x=2\)
___________
\(\left(4x-1\right)^2=121\)
\(\Rightarrow\left(4x-1\right)^2=11^2\)
\(\Rightarrow\left[{}\begin{matrix}4x-1=11\\4x-1=-11\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}4x=12\\4x=-10\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{5}{2}\end{matrix}\right.\)