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a) \(3\left(2x-1\right)+1=\left(-2\right)^2-3\left(-2\right)^3\)
\(\Leftrightarrow6x-3+1=4+24\)
\(\Leftrightarrow6x=4+24-1+3\)
\(\Leftrightarrow6x=30\)
\(\Leftrightarrow x=5\)
b) \(\left(x-2\right)\left(x+3\right)>0\)
\(\Leftrightarrow\orbr{\begin{cases}x-2>0\\x+3>0\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x>2\\x>-3\end{cases}}\)
c) \(x^2\left(x+2\right)-9\left(x+2\right)=0\)
\(\Leftrightarrow\left(x^2-9\right)\left(x+2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x^2-9=0\\x+2=0\end{cases}}\)\(\Leftrightarrow\orbr{\begin{cases}x=\pm3\\x=-2\end{cases}}\)
a) Ta có \(\hept{\begin{cases}x^2\ge0\forall x\\\left(y-\frac{1}{3}\right)^2\ge0\forall y\end{cases}\Rightarrow}x^2+\left(y-\frac{1}{3}\right)^2\ge0\forall x;y\)
Dấu "=" xảy ra <=> \(\hept{\begin{cases}x=0\\y-\frac{1}{3}=0\end{cases}}\Rightarrow\hept{\begin{cases}x=0\\y=\frac{1}{3}\end{cases}}\)
Vậy x = 0 ; y = 1/3 là giá trị cần tìm
b) Ta có : \(\hept{\begin{cases}\left|2x-1\right|\ge0\forall x\\\left|x-3y+2\right|\ge0\forall x;y\end{cases}}\Rightarrow\left|2x-1\right|+\left|x-3y+2\right|\ge0\forall x;y\)
Dấu "=" xảy ra <=> \(\hept{\begin{cases}2x-1=0\\x-3y+2=0\end{cases}}\Rightarrow\hept{\begin{cases}x=\frac{1}{2}\\-3y=-\frac{3}{2}\end{cases}}\Rightarrow\hept{\begin{cases}x=\frac{1}{2}\\y=\frac{1}{2}\end{cases}}\)
Vạy \(x=y=\frac{1}{2}\)là giá trị cần tìm
a) Ta có : \(\hept{\begin{cases}x^2\ge0\forall x\\\left(y-\frac{1}{3}\right)^2\ge0\forall y\end{cases}}\Rightarrow x^2+\left(y-\frac{1}{3}\right)^2\ge0\forall x,y\)
Kết hợp với đề bài => Chỉ xảy ra trường hợp x2 + ( y - 1/3 )2 = 0
=> x = 0 ; y = 1/3
b) \(\hept{\begin{cases}\left|2x-1\right|\\\left|x-3y+2\right|\end{cases}\ge}0\forall x,y\Rightarrow\left|2x-1\right|+\left|x-3y+2\right|\ge0\forall x,y\)
Dấu "=" xảy ra khi x = 1/2 ; y = 5/6
Đăng từng bài thoy nha pn!!!
Bài 1:
Có : 2009 = 2008 + 1 = x + 1
Thay 2009 = x + 1 vào biểu thức trên,ta có :
x\(^5\)- 2009x\(^4\)+ 2009x\(^3\)- 2009x\(^2\)+ 2009x - 2010
= x\(^5\)- (x + 1)x\(^4\)+ (x + 1)x\(^3\)- (x +1)x\(^2\)+ (x + 1) x - (x + 1 + 1)
= x\(^5\)- x\(^5\)- x\(^4\)+ x\(^4\)- x\(^3\)+ x\(^3\)- x\(^2\)+ x\(^2\)+ x - x -1 - 1
= -2
dễ
ai đi qua tick cho mình nha
ai tick thì may mắn trọn đời
B(x)=5x2+x-5
=>2B(x)=2(5x2+x-5)
=>2B(x)=10x2+2x-10
+)Ta có : C(x)-2B(x)=A(x)
=>C(x)=A(x)+2B(x)
A(x)+2B(x)=(3x3+3x2+2x-1)+(10x2+2x-10)
A(x)+2B(x)=3x3+3x2+2x-1+10x2+2x-10
A(x)+2B(x)=3x3+(3x2+10x2)+(2x+2x)+(-1-10)
A(x)+2B(x)=3x3+13x2+4x-11
=> C(x)=3x3+13x2+4x-11
\(A\left(x\right)=3x^3+3x^2+2x-1\)
\(B\left(x\right)=5x^2+x-5\)
Ta có : \(C\left(x\right)-2B\left(x\right)=A\left(x\right)\)
\(\Leftrightarrow C\left(x\right)-10x^2+2x-10=3x^3+3x^2+2x-1\)
\(\Leftrightarrow C\left(x\right)=-10x^2+2x-10-3x^3-3x^2-2x+1=0\)
\(\Leftrightarrow C\left(x\right)=-13x^2-9-3x^3=0\)
Vậy \(C\left(x\right)=-13x^2-9-3x^3\)
a) \(\left(x-1\right)^3=27\Leftrightarrow\left(x-1\right)^3=3^3\Leftrightarrow x-1=3\Leftrightarrow x=4\)
b) \(x^2+x=0\Leftrightarrow x\left(x+1\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x+1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=-1\end{cases}}\)
c) \(\left(2x+1\right)^2=25\Leftrightarrow\left(2x+1\right)^2=5^2\Leftrightarrow\orbr{\begin{cases}2x+1=5\\2x+1=-5\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=2\\x=-3\end{cases}}\)
d)\(\left(2x-3\right)^2=36\Leftrightarrow\left(2x-3\right)^2=6^2\Leftrightarrow\orbr{\begin{cases}2x-3=6\\2x-3=-6\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{9}{2}\\x=-\frac{3}{2}\end{cases}}}\)
a, x3 + 3x2 = 0
x2( x + 3 ) = 0
\(\Rightarrow\)x2 = 0 hoặc x + 3 = 0
x = 0 ____x = 0 - 3 =-3
b, x2 - 2x = 0
x ( x - 2 ) = 0
\(\Rightarrow\)x = 0 hoặc x - 2 = 0
x = 0+ 2 = 2
( #EXOComingSoon )
TH1: a+b+c khác 0
\(\frac{a+b-c}{c}=\frac{b+c-a}{a}=\frac{c+a-b}{b}\)
\(\Rightarrow2+\frac{a+b-c}{c}=2+\frac{b+c-a}{a}=2+\frac{c+a-b}{b}\)
\(\Rightarrow\frac{a+b+c}{c}=\frac{a+b+c}{a}=\frac{a+b+c}{b}\)
\(\Rightarrow a=b=c\)
thay a=b=c vào B ta có:
\(B=\left(1+\frac{a}{a}\right)\cdot\left(1+\frac{a}{a}\right)\cdot\left(1+\frac{a}{a}\right)=2\cdot2\cdot2=8\)
TH2: a+b+c=0
=> c=-a-b
=>a=-b-c
=>b=-a-c
thay a,b,c vào B ta có:
\(B=\left(1+\frac{-\left(a+c\right)}{a}\right)\cdot\left(1+\frac{-\left(b+c\right)}{c}\right)\cdot\left(1+\frac{-\left(a+b\right)}{b}\right)\)
\(B=\left(-\frac{c}{a}\right)\cdot\left(-\frac{b}{c}\right)\cdot\left(-\frac{a}{b}\right)=-1\)
p/s: th2 ko chắc nhá
a = ???
\(b,3x+x^2=0\\ \Rightarrow x\left(3+x\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=-3\end{matrix}\right.\\ c,\left(x-1\right)\left(x-3\right)< 0\\ \Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-1< 0\\x-3>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-1>0\\x-3< 0\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x< 1\\x>3\left(vô.lí\right)\end{matrix}\right.\\\left\{{}\begin{matrix}x>1\\x< 3\end{matrix}\right.\end{matrix}\right.\)
Vậy 1<x<3