A = x² - 10x + 12

= ( x² - 10x + 25 ) - 13

= ( x - 5 )² - 13

( x - 5 )² ≥ 0 ∀ x => ( x - 5 )² - 13 ≥ -13

Đẳng thức xảy ra <=> x - 5 = 0 => x = 5

=> MinA = -13 <=> x = 5

B = 6y² + 4y - 1

= 6( y² + 2/3y + 1/9 ) - 5/3

= 6( y + 1/3 )² - 5/3

6( y + 1/3 )² ≥ 0 ∀ x => 6( y + 1/3 )² - 5/3 ≥ -5/3

Đẳng thức xảy ra <=> y + 1/3 = 0 => y = -1/3

=> MinB = -5/3 <=> y = -1/3

C = x² + y² - 2x - 6y - 1

= ( x² - 2x + 1 ) + ( y² - 6y + 9 ) - 11

= ( x - 1 )² + ( y - 3 )² - 11

\(\hept{\begin{cases}\left(x-1\right)^2\ge0\forall x\\\left(y-3\right)^2\ge0\forall y\end{cases}\Rightarrow}\left(x-1\right)^2+\left(y-3\right)^2-11\ge-11\)

Đẳng thức xảy ra <=> \(\hept{\begin{cases}x-1=0\\y-3=0\end{cases}}\Rightarrow\hept{\begin{cases}x=1\\y=3\end{cases}}\)

=> MinC = -11 <=> x = 1 ; y = 3

D = 2x² + 3y² - x - 3y + 5

= 2( x² - 1/2x + 1/16 ) + 3( y² - y + 1/4 ) + 33/8

= 2( x - 1/4 )² + 3( y - 1/2 )² + 33/8

\(\hept{\begin{cases}2\left(x-\frac{1}{4}\right)^2\ge0\forall x\\3\left(y-\frac{1}{2}\right)^2\ge0\forall y\end{cases}}\Rightarrow2\left(x-\frac{1}{4}\right)^2+3\left(y-\frac{1}{2}\right)^2+\frac{33}{8}\ge\frac{33}{8}\)

Đẳng thức xảy ra <=> \(\hept{\begin{cases}x-\frac{1}{4}=0\\y-\frac{1}{2}=0\end{cases}}\Rightarrow\hept{\begin{cases}x=\frac{1}{4}\\y=\frac{1}{2}\end{cases}}\)

=> MinD = 33/8 <=> x = 1/4 ; y = 1/2

You're the best

Lan is my best friend

cứ làm đi 3 con tích sẽ về ngay tay bn

Bài 1:

G/s ngược lại: \(ad=bc\) , ta cần CM giả thiết.

Ta có: \(ad=bc\) => \(\frac{a}{b}=\frac{c}{d}=k\Rightarrow\hept{\begin{cases}a=bk\\c=dk\end{cases}}\) \(\left(k\inℤ\right)\)

Thay vào:

\(\left(a+b+c+d\right)\left(a-b-c+d\right)\)

\(=\left(bk+b+dk+d\right)\left(bk-b-dk+d\right)\)

\(=\left(k+1\right)\left(b+d\right)\left(k-1\right)\left(b-d\right)\) (1)

\(\left(a-b+c-d\right)\left(a+b-c-d\right)\)

\(=\left(bk-b+dk-d\right)\left(bk+b-dk-d\right)\)

\(=\left(k-1\right)\left(b+d\right)\left(k+1\right)\left(b-d\right)\) (2)

Từ (1) và (2) => GT được CM => đpcm

It's coffin.

reasonable

c, ta có: \(2^{4n+2}\)+1\(⋮\)5

=> (...6).(\(2^2\))+1\(⋮\)5 

=>(...6).4+1\(⋮\)5

=>(...24)+1\(⋮\)5

=>(...25)\(⋮\)5 =>(đpcm)

XV. Reorder the words to make meaningful sentences
. 1. V cheat/ never/ will/ the/ promisel exam/ that1/ in anymore.=>V  promise that will never cheat the exam anymore (câu này bạn chép vào hình như không đủ câu hoặc thiếu chéo)
2. swim/ she/ after/ able/ will/ be/ to/ praces/ hard two/ i0 shel weeks.=> She will be able to praces swim hard in two week  

3. we/ if our/ planta environment/ bel greener/ more/ trees will=>If we plant more trees,our environment will be more greener

. 4. fly/ I/ my/ buy/ a ket/ to / could/ to New York/ holiday for.=> I could buy a ket fly to New York for my holiday

5. take/ this/ probably/ he/ environment/ will part/ in/ campaign.=> He probaly will take part in this environment campaign

. XVI. Rewrite the sentences based on the given words helow

. 1.1 was able to ride a bicycle when I was 7 years old(Câu này không có từ cho ?)

.I I couldn't visit Glasgow because I didn't have enough time.I.. (able) => I can't be able visited  Glasgow because have enough time

3. I want to have a private tutor. I will learn better. IfI have =>If I have a private tutor,I will learn better

4. Some robots in the future will have the ability to do all the housework. Some robots . (able) => Some robots will be able have the ability to do all the house work

5. Maybe he will paripate in this recycling campaign. -> He will... (probably

What would she ?

She'd some water

<=> What some she did ?