Tính giá trị của biểu thức :
A = 27x3 + 54x2 + 36x + 4 với x = -2002
B = 2x2 + 4x + xy + 2y với x = 88, y = -76
K
Khách
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Những câu hỏi liên quan
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
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
Z
7 tháng 8 2016
a) A=(2X^2+XY)+(4X+2Y)
=X(2X+Y) + 2(2X+Y)
= (2X+Y)(2+X)
Thay X=88,Y=-76
A=(2*88-76)(2+88)=100*90=9000
b) nhóm X^2 với -7X,XY với -7Y,làm tương tự thì B=6
23 tháng 5 2022
Bài 2:
a: \(A=\left[a+\left(b-c\right)\right]^2+\left[a-\left(b-c\right)\right]^2\)
\(=a^2+2a\left(b-c\right)+\left(b-c\right)^2+a^2-2a\left(b-c\right)+\left(b-c\right)^2\)
\(=2a^2+2\left(b-c\right)^2\)
\(=2\cdot1^2+2\left(3+1\right)^2=2+32=34\)
b: \(B=a^2+2ab+b^2-a^2+2ab-b^2=4ab=4\cdot2\cdot5=40\)
H9
HT.Phong (9A5)
CTVHS
7 tháng 10 2023
a) ĐKXĐ: \(x\ne2y,x\ne-y;x\ne-1\)
b) \(B=\left(\dfrac{x-y}{2y-x}-\dfrac{x^2+y^2+y-2}{x^2-xy-2y^2}\right):\dfrac{4x^4+4x^2y+y^2-4}{x^2+y+xy+x}\)
\(B=\left[\dfrac{y-x}{x-2y}-\dfrac{x^2+y^2+y-2}{\left(x+y\right)\left(x-2y\right)}\right]:\dfrac{4x^4+4x^2y+y^2-4}{x\left(x+y\right)+\left(x+y\right)}\)
\(B=\left[\dfrac{\left(y-x\right)\left(x+y\right)}{\left(x-2y\right)\left(x+y\right)}-\dfrac{x^2+y^2+y-2}{\left(x+y\right)\left(x-2y\right)}\right]:\dfrac{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}{\left(x+1\right)\left(x+y\right)}\)
\(B=\dfrac{y^2-x^2-x^2-y^2-y+2}{\left(x+y\right)\left(x-2y\right)}:\dfrac{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}{\left(x+1\right)\left(x+y\right)}\)
\(B=\dfrac{-2x^2-y+2}{\left(x+y\right)\left(x-2y\right)}\cdot\dfrac{\left(x+1\right)\left(x+y\right)}{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}\)
\(B=\dfrac{-\left(2x^2+y-2\right)}{\left(x+y\right)\left(x-2y\right)}\cdot\dfrac{\left(x+1\right)\left(x+y\right)}{\left(2x^2+y+2\right)\left(2x^2+y-2\right)}\)
\(B=\dfrac{-\left(x+1\right)}{\left(x-2y\right)\left(2x^2+y+2\right)}\)
LK
1
20 tháng 8 2021
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: \(\left(x+3\right)\cdot\left(x^2-3x+5\right)=x^2+3x\)
\(\Leftrightarrow\left(x+3\right)\cdot\left(x^2-4x+5\right)=0\)
\(\Leftrightarrow x=-3\)
16 tháng 3 2022
\(N=3x^4+3x^2y^2+x^2y^2+y^4+2y^2\)
\(=\left(x^2+y^2\right)\left(3x^2+y^2\right)+2y^2\)
\(=3x^2+3y^2=3\)
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
\(d,x^6-1=0\\ \Leftrightarrow\left(x^2\right)^3-1^3=0\\ \Leftrightarrow\left(x^2-1\right)\left(x^4+x^2+1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x^4+x^2+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+1=0\\x^4+x^2+1=0\left(Vô.lí,vì:x^4\ge0;x^2\ge0,\forall x\in R\right)\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\\ c,\left(x^3+8\right)-\left(x+2\right)\left(x-4\right)=0\\ \Leftrightarrow\left(x^3+8\right)-\left(x^2-2x-8\right)=0\\ \Leftrightarrow x^3-x^2+2x+16=0\\ \Leftrightarrow x^3+2x^2-3x^2-6x+8x+16=0\\ \Leftrightarrow x^2\left(x+2\right)-3x\left(x+2\right)+8\left(x+2\right)=0\\ \Leftrightarrow\left(x^2-3x+8\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2-3x+8=0\left(Vô.lí\right)\\x+2=0\end{matrix}\right.\Leftrightarrow x=-2\)
a, A = 27x3 + 54x2 + 36x + 4
=> A = (3x)3 + 2 . 3 . 9x2 + 3 . 3x . 4 + 8 - 4
=> A = [(3x)3 + 2 . 3 . (3x)2 + 3 . 3x . 22 + 23] - 4
=> A = (3x + 2)3 - 4
Thay x = -2002 vào A ta có: A = (3x + 2)3 - 4
=> A = [3 x (-2002) + 2]3 - 4 = [6006 + 2]3 - 4 = 60083 - 4
b, B = 2x2 + 4x + xy + 2y
=> B = 2x(x + 2) + y(x + 2)
=> B = (x + 2)(2x + y)
Thay x = 88; y = -76 vào B
=> B = (88 + 2)[2 . 88 + (-76)]
=> B = 90 . [176 + (-76)] = 90 . 100 = 9000