Giải giúp em bài 1,2
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1.
\(P=\dfrac{3}{\sqrt{x}+3}\le\dfrac{3}{0+3}=1\)
\(\Rightarrow maxP=1\Leftrightarrow x=0\)
2.
\(A=\dfrac{2\sqrt{x}-1}{\sqrt{x}+1}=\dfrac{2\left(\sqrt{x}+1\right)-3}{\sqrt{x}+1}=2-\dfrac{3}{\sqrt{x}+1}\ge2-\dfrac{3}{0+1}=-1\)
\(\Rightarrow minA=-1\Leftrightarrow x=0\)
\(a,\Leftrightarrow\Delta'=\left(m-1\right)^2-\left(m-2\right)\ge0\\ \Leftrightarrow m^2-3m+3\ge0\\ \Leftrightarrow\left(m-\dfrac{3}{2}\right)^2+\dfrac{3}{4}\ge0\left(\text{luôn đúng}\right)\)
Vậy PT có 2 nghiệm pb với mọi m
\(b,\Leftrightarrow0< x_1< x_2\Leftrightarrow\left\{{}\begin{matrix}x_1+x_2>0\\x_1x_2>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2\left(m-1\right)>0\\m-2>0\end{matrix}\right.\Leftrightarrow m>2\\ c,\text{Thay }x=2\Leftrightarrow4-4\left(m-1\right)+m-2=0\\ \Leftrightarrow m=2\\ \Leftrightarrow x^2-2x=0\\ \Leftrightarrow x\left(x-2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\\ d,\text{Viét: }\left\{{}\begin{matrix}x_1+x_2=2\left(m-1\right)\\x_1x_2=m-2\end{matrix}\right.\\ x_1^2+x_2^2=8\Leftrightarrow\left(x_1+x_2\right)^2-2x_1x_2=8\\ \Leftrightarrow4\left(m-1\right)^2-2\left(m-2\right)=8\\ \Leftrightarrow4m^2-10m=0\\ \Leftrightarrow m\left(2m-5\right)=0\Leftrightarrow\left[{}\begin{matrix}m=0\\m=\dfrac{5}{2}\end{matrix}\right.\)
Bài 1:
X x 0,25 + X : 0,25 = 4,59
X x 0,25 + X x 4 = 4,59
X x ( 0,25 + 4 ) = 4,59
X x 4,25 = 4,59
X = 4,59 : 4,25
X = 1,08
Bài 2 :
X : 0,1 - 9,9 = X x 0,1 - 9,9
X x 10 - 9,9 = X x 0,1 - 9,9
X x 10 - X x 0,1 = 9,9 - 9,9
X x ( 10 - 0,1 ) = 0
X x 9,9 = 0
X = 0 : 9,9
X = 0
Bài 3 :
Cách 1 :
1,2 x 3,4 : 0,5 = ( 1,2 : 0,5 ) x 3,4 = 2,4 x 3,4 = 8,16
Cách 2 :
1,2 x 3,4 : 0,5 = 4,08 : 0,5 = 8,16
Cách 3 :
1,2 x 3,4 : 0,5 = 1,2 x ( 3,4 : 0,5 ) = 1,2 x 6,8 = 8,16
bài 1:
X x 0,25 + X x 1/0,25=4,59
X x(0,25 + 1/0,25)=4,59
X x [(0,0625+1)/ 0,25]=4,59
X x (1,0625/ 0,25)=4,59
X x 4,25=4,59
X= 4,59 / 4,25
X=1,08
bài 2:
X : 0,1- X x 0,1=-9,9+9,9
X x 1/0,1- X x0,1=0
X x(1/ 0,1 -0,1)=0
X x [(1- 0,01)/ 0,1]=0
X x 0,99/0,1=0
X x 9,9 =0
X=0
Bài 1.
a) Ta có
\(f\left(x\right)=9-x^5+4x-2x^3+x^2-7x^4\\ f\left(x\right)=-x^5-7x^4-2x^3+x^2+4x+9\)
Lại có:
\(g\left(x\right)=x^5-9+2x^2+7x^4+2x^3-3x\\ g\left(x\right)=x^5+7x^4+2x^3+2x^2-3x-9\)
b) \(h\left(x\right)=f\left(x\right)+g\left(x\right)\)
\(h\left(x\right)=\left(-x^5+x^5\right)+\left(-7x^4+7x^4\right)+\left(-2x^3+2x^3\right)+\left(x^2+2x^2\right)+\left(4x-3x\right)+\left(9-9\right)\)
\(h\left(x\right)=3x^2+x\)
c) \(h\left(x\right)=0\)
\(3x^2+x=0\)
\(x\left(3x+1\right)=0\)
TH1: \(x=0\)
TH2: \(3x+1=0\) hay \(x=-\dfrac{1}{3}\)
Vậy nghiệm của \(h\left(x\right)\) là \(x=0;x=-\dfrac{1}{3}\)
Bài 2.
a) Ta có \(\left\{{}\begin{matrix}A\left(x\right)=6x^3+5x^2\\B\left(x\right)=x^3-x^2\\C\left(x\right)=-2x^3+4x^2\end{matrix}\right.\)
\(D\left(x\right)=A\left(x\right)+B\left(x\right)-C\left(x\right)\)
\(D\left(x\right)=\left(6x^3+x^3-\left(-2x^3\right)\right)+\left(5x^2-x^2-4x^2\right)\)
\(D\left(x\right)=9x^3\)
b) \(D\left(x\right)=0\)
\(9x^3=0\\ x^3=0\\ x=0\)
Vậy nghiệm của đa thức \(D\left(x\right)\) là \(x=0\).
1
a
\(=x\left(x^2+xy\right)-z\left(x^2+xy\right)\\ =\left(x-z\right)\left(x^2+xy\right)\)
b
\(=12\left(xy-xz\right)+3x\left(xy-xz\right)\\ =\left(12+3x\right)\left(xy-xz\right)\\ =x\left(12+3x\right)\left(y-z\right)\)
c
\(=\dfrac{1}{2}\left(x^4+2x^2y^2+y^4\right)-\dfrac{1}{2}.4x^2y^2\\ =\dfrac{1}{2}\left(x^4+2x^2y^2+y^4-4x^2y^2\right)\\ =\dfrac{1}{2}\left(x^4-2x^2y^2+y^4\right)\\ =\dfrac{1}{2}\left(x^2-y^2\right)^2\\ =\dfrac{1}{2}\left(x^2-y^2\right)\left(x^2-y^2\right)\\ =\dfrac{1}{2}\left(x-y\right)\left(x+y\right)\left(x-y\right)\left(x+y\right)\)
d
\(=2\left(x-y\right)^2-2.\left(5xy\right)^2\\ =2\left[\left(x-y\right)^2-\left(5xy\right)^2\right]\\ =2\left(x-y-5xy\right)\left(x-y+5xy\right)\)
2
\(5x^2z-10xyz+5y^2z\\ =5x^2z-5xyz-5xyz+5y^2z\\ =\left(5x^2z-5xyz\right)-\left(5xyz-5y^2z\right)\\ =5xz\left(x-y\right)-5yz\left(x-y\right)\\ =\left(5xz-5yz\right)\left(x-y\right)\\ =5z\left(x-y\right)\left(x-y\right)\\=5z\left(x-y\right)^2\)
Thế \(x=124;y=24;z=2\) vào biểu thức được:
\(5.2\left(124-24\right)^2=10.\left(100\right)^2=10.10000=100000\)
Đăng tách ra bạn nhé
Vì AD là pg \(\dfrac{AB}{AC}=\dfrac{BD}{DC}\Rightarrow\dfrac{5}{4}=\dfrac{3}{DC}\Rightarrow DC=\dfrac{12}{5}cm\)
BC = DC + DB = 12/5 + 3 = 27/5 cm
chọn B
Câu 1:
\(PTHH:C+O_2\xrightarrow{t^o}CO_2\\ Si+O_2\xrightarrow{t^o}SiO_2\\ 4P+5O_2\xrightarrow{t^o}2P_2O_5\\ 2Zn+O_2\xrightarrow{t^o}2ZnO\\ 2Cu+O_2\xrightarrow{t^o}2CuO\)
Câu 2:
\(a,2H_2+O_2\xrightarrow{t^o}2H_2O\\ b,2Ca+O_2\xrightarrow{t^o}2CaO\\ c,S+O_2\xrightarrow{t^o}SO_2\\ d,2Ba+O_2\xrightarrow{t^o}2BaO\)