the sun rises in the east

water boils at 100 centigrade degrees

the weather is not warm enough to go swimming

I'd like to go on holiday but I haven't got enough money

he isn't experienced enough to do the job

the earth moves round the sun

I'm lucky enough to have a lot of friends

each of them has a different character
she has big brown eyes

his daughter has long blond hair

Bài 1:

\(a,A=\dfrac{22}{7}-\dfrac{22}{7}-0,25-0,75-4=-1-4=-5\\ b,B=\dfrac{1\cdot\left(\dfrac{2}{5}\right)^3\cdot\left(\dfrac{15}{4}\right)^2}{\left(\dfrac{15}{2^2}\right)^2\cdot\left(\dfrac{2}{5}\right)^3}=1\)

Bài 2:

\(a,\Rightarrow2^{x+3}=13,9+2,1=16=2^4\\ \Rightarrow x+3=4\Rightarrow x=1\\ b,\Rightarrow\left|x-\dfrac{3}{2}\right|=0,5=\dfrac{1}{2}\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}+\dfrac{3}{2}=2\\x=-\dfrac{1}{2}+\dfrac{3}{2}=1\end{matrix}\right.\\ c,\Rightarrow\dfrac{x}{2}=\dfrac{y}{7}=\dfrac{2x-5y}{2\cdot2-5\cdot7}=\dfrac{93}{-31}=-3\\ \Rightarrow\left\{{}\begin{matrix}x=-6\\y=-21\end{matrix}\right.\)

a: Q(x)=5x^2-2x+1

Q(1)=5-2+1=4

Q(-1)=5+2+1=8

Q(2)=5*2^2-2*2+1=5*4-4+1=16+1=17

Q(-2)=5*(-2)^2-2*(-2)+1=5*4+2*2+1=25

Q(0)=1

b: R(x)=-x^2+2x-10

R(1)=-1+2-10=1-10=-9

R(-1)=-(-1)^2+2(-1)-10=-1-2-10=-13

R(2)=-4+6-10=-8

R(-2)=-4-6-10=-20

R(0)=-10

d: P(x)=6x^5-4x^3+9x^2-2x+2

P(2)=6*2^5-4*2^3+9*2^2-2*2+2=194

P(-2)=6*(-2)^5-4*(-2)^3+9*(-2)^2-2*(-2)+2=-118

P(0)=2

P(1)=6-4+9-2+2=11

P(-1)=-6+4+9+2+2=11

a) \(\left\{{}\begin{matrix}\left(m-1\right)x+y=2\\mx+y=m+1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(m-1\right)x+y=2\\\left(m-1\right)-mx=2-\left(m+1\right)\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\left(m-1\right)x+y=2\\-x=1-m\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(m-1\right)^2+y=2\\x=m-1\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}y=2-\left(m-1\right)^2\\x=m-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-m^2+2m+1\\x=m-1\end{matrix}\right.\)

\(2x+y=2\left(m-1\right)+\left(-m^2+2m+1\right)=2m-2-m^2+2m+1=-m^2+4m-1=-\left(m^2-4m+4\right)+3=-\left(m-2\right)^2+3\le3\)

Dấu "=" xảy ra \(\Leftrightarrow m=2\)

\(a,HPT\Leftrightarrow\left\{{}\begin{matrix}mx-x+y=2\\mx+y=m+1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}mx+y=x+2\\mx+y=m+1\end{matrix}\right.\\ \Leftrightarrow x+2=m+1\Leftrightarrow x=m-1\\ \Leftrightarrow\left(m-1\right)^2+y=2\\ \Leftrightarrow y=2-\left(m-1\right)^2\)

\(2x+y\le3\\ \Leftrightarrow2m-2+2-m^2+2m-1-3\le0\\ \Leftrightarrow-m^2+4m-4\le0\\ \Leftrightarrow-\left(m-2\right)^2\le0\left(luôn.đúng\right)\)

Vậy ta được đpcm

b, \(x+y=-4\Leftrightarrow x=-4-y\Leftrightarrow\left\{{}\begin{matrix}m-1=-4-y\left(1\right)\\y=2-\left(m-1\right)^2\left(2\right)\end{matrix}\right.\)

Thế (2) vào (1)

\(\Leftrightarrow m-1=-4-2+\left(m-1\right)^2\\ \Leftrightarrow m-1=-6+m^2-2m+1\\ \Leftrightarrow m^2-3m-4=0\\ \Leftrightarrow\left[{}\begin{matrix}m=-1\\m=4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}y=2-4=-2\\y=2-9=-7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=3\end{matrix}\right.\)

Vậy \(\left(x;y\right)=\left\{\left(-2;-2\right);\left(3;-7\right)\right\}\)

Tham khảo:

\(a,\Leftrightarrow\Delta'=\left(m-1\right)^2-\left(m-2\right)\ge0\\ \Leftrightarrow m^2-3m+3\ge0\\ \Leftrightarrow\left(m-\dfrac{3}{2}\right)^2+\dfrac{3}{4}\ge0\left(\text{luôn đúng}\right)\)

Vậy PT có 2 nghiệm pb với mọi m

\(b,\Leftrightarrow0< x_1< x_2\Leftrightarrow\left\{{}\begin{matrix}x_1+x_2>0\\x_1x_2>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2\left(m-1\right)>0\\m-2>0\end{matrix}\right.\Leftrightarrow m>2\\ c,\text{Thay }x=2\Leftrightarrow4-4\left(m-1\right)+m-2=0\\ \Leftrightarrow m=2\\ \Leftrightarrow x^2-2x=0\\ \Leftrightarrow x\left(x-2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\\ d,\text{Viét: }\left\{{}\begin{matrix}x_1+x_2=2\left(m-1\right)\\x_1x_2=m-2\end{matrix}\right.\\ x_1^2+x_2^2=8\Leftrightarrow\left(x_1+x_2\right)^2-2x_1x_2=8\\ \Leftrightarrow4\left(m-1\right)^2-2\left(m-2\right)=8\\ \Leftrightarrow4m^2-10m=0\\ \Leftrightarrow m\left(2m-5\right)=0\Leftrightarrow\left[{}\begin{matrix}m=0\\m=\dfrac{5}{2}\end{matrix}\right.\)