tìm x, biết :
a) 27x3 -54x2 +36x=8
b) (x+3) (x2 -3x +5)= x2 +3x
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ND
Nguyễn Đức Trí
VIP
3 tháng 8 2023
a) \(\left(x-5\right)^2=\left(3+2x\right)^2\)
\(\Rightarrow\left(3+2x\right)^2-\left(x-5\right)^2=0\)
\(\Rightarrow\left(3+2x+x-5\right)\left(3+2x-x+5\right)=0\)
\(\Rightarrow\left(3x-2\right)\left(x+8\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}3x-2=0\\x+8=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=-8\end{matrix}\right.\)
b) \(27x^3-54x^2+36x=9\)
\(\Rightarrow27x^3-54x^2+36x-9=0\)
\(\Rightarrow27x^3-54x^2+36x-8+8-9=0\)
\(\Rightarrow\left(3x-2\right)^3-1=0\)
\(\Rightarrow\left(3x-2-1\right)\left[\left(3x-2\right)^2+3x-2+1\right]=0\)
\(\Rightarrow\left(3x-3\right)\left[\left(3x-2\right)^2+3x-2+\dfrac{1}{4}-\dfrac{1}{4}+1\right]=0\)
\(\Rightarrow\left(3x-3\right)\left[\left(3x-2+\dfrac{1}{2}\right)^2+\dfrac{3}{4}\right]=0\)
\(\Rightarrow\left(3x-3\right)\left[\left(3x-\dfrac{3}{2}\right)^2+\dfrac{3}{4}\right]=0\left(1\right)\)
mà \(\left(3x-\dfrac{3}{2}\right)^2+\dfrac{3}{4}>0,\forall x\)
\(\left(1\right)\Rightarrow3x-3=0\Rightarrow3x=3\Rightarrow x=1\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
3 tháng 8 2023
(\(x-5\))2 = (3 +2\(x\))2 ⇒ \(\left[{}\begin{matrix}x-5=3+2x\\x-5=-3-2x\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}x=-8\\x=\dfrac{2}{3}\end{matrix}\right.\) vậy \(x\in\){-8; \(\dfrac{2}{3}\)}
27\(x^3\) - 54\(x^2\) + 36\(x\) = 9
27\(x^3\) - 54\(x^2\) + 36\(x\) - 8 = 1
(3\(x\) - 2)3 = 1 ⇒ 3\(x\) - 2 = 1 ⇒ \(x\) = 1
KK
4
XO
31 tháng 7 2023
a) (2x - 5)2 - (5 + 2x) = 0
<=> 4x2 - 22x + 20 = 0
\(\Leftrightarrow\left(2x-\dfrac{11}{2}\right)^2=\dfrac{41}{4}\)
\(\Leftrightarrow x=\dfrac{\pm\sqrt{41}+11}{4}\)
b) \(27x^3-54x^2+36x=0\)
\(\Leftrightarrow x\left(3x^2-6x+4\right)=0\)
\(\Leftrightarrow x=0\) (Vì \(3x^2-6x+4=3\left(x-1\right)^2+1>0\forall x\))
c) x3 + 8 - (x + 2).(x - 4) = 0
\(\Leftrightarrow\left(x+2\right).\left(x^2-2x+4\right)-\left(x+2\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x^2-3x+8\right)=0\)
\(\Leftrightarrow x=-2\) (Vì \(x^2-3x+8=\left(x-\dfrac{3}{2}\right)^2+\dfrac{23}{4}>0\))
d) \(x^6-1=0\)
\(\Leftrightarrow\left(x^2\right)^3-1=0\)
\(\Leftrightarrow\left(x^2-1\right)\left(x^4+x^2+1\right)=0\)
\(\Leftrightarrow x^2-1=0\) (Vì \(x^4+x^2+1>0\))
\(\Leftrightarrow x=\pm1\)
GN
GV Nguyễn Trần Thành Đạt
Giáo viên
31 tháng 7 2023
\(d,x^6-1=0\\ \Leftrightarrow\left(x^2\right)^3-1^3=0\\ \Leftrightarrow\left(x^2-1\right)\left(x^4+x^2+1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x^4+x^2+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+1=0\\x^4+x^2+1=0\left(Vô.lí,vì:x^4\ge0;x^2\ge0,\forall x\in R\right)\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\\ c,\left(x^3+8\right)-\left(x+2\right)\left(x-4\right)=0\\ \Leftrightarrow\left(x^3+8\right)-\left(x^2-2x-8\right)=0\\ \Leftrightarrow x^3-x^2+2x+16=0\\ \Leftrightarrow x^3+2x^2-3x^2-6x+8x+16=0\\ \Leftrightarrow x^2\left(x+2\right)-3x\left(x+2\right)+8\left(x+2\right)=0\\ \Leftrightarrow\left(x^2-3x+8\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2-3x+8=0\left(Vô.lí\right)\\x+2=0\end{matrix}\right.\Leftrightarrow x=-2\)
NL
1
18 tháng 8 2023
a: A=(2x-1)^3
Khi x=5,5 thì A=(2*5,5-1)^3=10^3=1000
b: B=27x^3+54x^2+36x+7
=(3x)^3+3*(3x)^2*2+3*3x*2^2+2^3-1
=(3x+2)^3-1
=(-8+2)^3-1
=(-6)^3-1=-217
DP
1
30 tháng 9 2021
a)
\(\left(3x\right)^3-3.\left(3x\right)^2.1+3.3x.2^2-2^3=0\)
\(\left(3x-2\right)^3=0\)
3x-2=0
3x=2
x=2/3
b)
\(x^3-3.x^2.5+3.x.5^2+5^3=0\)
\(\left(x-5\right)^3=0\)
x-5=0
x=5
MH
16 tháng 9 2021
a) \(\left(x-1\right)^3\)
\(=x^3-3x^2+3x-1\)
b) \(\left(2x-3y\right)^3\)
\(=\left(2x\right)^3-3\left(2x\right)^23y+3.2x\left(3y\right)^3+\left(3y\right)^3\)
\(=8x^3-36x^2y+54xy^2-27y^3\)
16 tháng 9 2021
Bài 3:
a: Ta có: \(\left(x-2\right)^3-x^2\left(x-6\right)=5\)
\(\Leftrightarrow x^3-6x^2+12x-8-x^3+6x^2=5\)
\(\Leftrightarrow12x=13\)
hay \(x=\dfrac{13}{12}\)
b: Ta có: \(\left(x-1\right)\left(x^2+x+1\right)-x\left(x+2\right)\left(x-2\right)=4\)
\(\Leftrightarrow x^3-1-x^3+4x=4\)
\(\Leftrightarrow4x=5\)
hay \(x=\dfrac{5}{4}\)
CM
31 tháng 1 2017
a) (x - 1)(x - 2). b) 4(x - 2)(x - 7).
c) (x + 2)(2x +1). d) (x - l)(2x - 7).
e) (2x + 3y - 3)(2x - 3y +1). g) (x - 3)( x 3 + x 2 - x +1).
h) (x + y)(x + y-l)(x + y + l).
a: Ta có: \(27x^3-54x^2+36x=8\)
\(\Leftrightarrow27x^3-54x^2+36x-8=0\)
\(\Leftrightarrow\left(3x-2\right)^3=0\)
\(\Leftrightarrow3x-2=0\)
hay \(x=\dfrac{2}{3}\)
b: Ta có: \(\left(x+3\right)\cdot\left(x^2-3x+5\right)=x^2+3x\)
\(\Leftrightarrow\left(x+3\right)\cdot\left(x^2-4x+5\right)=0\)
\(\Leftrightarrow x=-3\)