Trong không gian với hệ tọa độ Oxyz lấy các điểm A(a;0;0), B(0;b;0), C(0;0;c) trong đó a > 0 ,   b > 0 ,   c > 0 và 1 a + 1 b + 1 c = 2 .  Khi a, b, c thay đổi, mặt phẳng (ABC) luôn đi qua một điểm cố định có tọa độ

A. (1;1;1)

B. (2;2;2)

C.  1 2 ; 1 2 ; 1 2

D. - 1 2 ; - 1 2 ; - 1 2

Bất phương trình dạng ax+b<0(hoặc ax+b>0, ax+b\(\le\)0, ax+b\(\ge\)0) trong đó a và b là hai số đã cho, a\(\ne\)0, được gọi là bất phương trình bậc nhất 1 ẩn.

a) x(x+4)(x-4)-(x²+1)(x²-1)

=x(x²-16)-x⁴+1=-x⁴+x³-16x+1

b) (a+b-c)²-(a-c)²-2ab+2bc

=(a+b-c-a+c)(a+b-c+a-c)-2ab+2bc

=b(2a+b-2c)-2ab+2bc

=2ab+b²-2bc-2ab+2bc

=b²

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Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions.

Southern Thailand was hit Thursday by the most severe haze from forest fires in Indonesia, forcing all schools in a province to close and disrupting flights in a popular tourist area, officially said.

The haze that has shrouded parts of Malaysia and Singapore for nearly two months reached hazardous levels in the southern Thai city of Songkhla, with the pollution index hitting a record-high reading of 365. A reading of 101-200 is unhealthy, 201-300 is very unhealthy and above 300 is hazardous.

“This is a crisis,” said Halem Jemarican, head of the Southern Environment Office. He said the pollution index in southern Thailand has never exceeded 300 before.
Halem said his office has worked with other authorities to have all schools in Songkhla province send students home and all outdoor sports stadiums to close temporarily. Warnings have been issued to vulnerable people such as children, the elderly and people with illnesses not to go out of their homes.

“The wind speed is very low this year in the south, causing haze to stay in our skies longer,” Halem said by telephone.

An airport official in Hat Yai, a popular tourist area, said three flights bound for Bangkok were delayed Thursday morning because of the haze. A flight from Bangkok to Hat Yai was diverted to Surat Thani on Wednesday evening. The official declined to be identified because of working rules.

Local media reported that cloud seeding has been discussed as a way to dispel the haze in southern Thailand, which is hundreds of kilometers (miles) from the forest fires in Indonesia's Sumatra island.

Southern Thailand boasts tropical beaches popular among tourists in Surat Thani and Phuket, two of the seven provinces suffering from the haze

Which statement is NOT true, according to the passage?

A. The pollution index in southern Thailand used to exceed 300

B. Seven provinces in Thailand suffered from the haze

C. The haze reached a hazardous level in the city of Songkhla

D. The local authorities warned the citizens against going out

1. (a²+b²+ab)²-a²b²-b²c²-c²a²

=a⁴+b⁴+a²b²+2(a²b²+ab³+a³b)-a²b²-b²c²-c²a²

=a⁴+b⁴+2a²b²+2ab³+2a³b-b²c²-c²a²

=(a²+b²)²+2ab(a²+b²)-c²(a²+b²)

=(a²+b²)[(a+b)²-c²]

=(a²+b²)(a+b+c)(a+b-c)

2. a⁴+b⁴+c⁴-2a²b²-2b²c²-2a²c²=(a²-b²-c²)²

3. a(b³-c³)+b(c³-a³)+c(a³-b³)

=ab³-ac³+bc³-ba³+ca³-cb³

=a³(c-b)+b³(a-c)+c³(b-a)

=a³(c-b)-b³(c-a)+c³(b-a)

=a³(c-b)-b³(c-b+b-a)+c³(b-a)

=a³(c-b)-b³(c-b)-b³(b-a)+c³(b-a)

=(c-b)(a-b)(a²+ab+b²)-(b-a)(b-c)(b²+bc+c²)

=(a-b)(c-b)(a²+ab+2b²+bc+c²)

4. a⁶-a⁴+2a³+2a²=a⁴(a+1)(a-1)+2a²(a+1)=(a+1)(a⁵-a⁴+2a²)=a²(a+1)(a³-a²+2)

5. (a+b)³-(a-b)³=(a+b-a+b)[(a+b)²+(a+b)(a-b)+(a-b)²]

=2b(3a²+b²)

6. x³-3x²+3x-1-y³=(x-1)³-y³=(x-1-y)[(x-1)²+(x-1)y+y²]

=(x-y-1)(x²+y²+xy-2x-y+1)

7. x^m+4+x^m+3-x-1=x^m+3(x+1)-(x+1)=(x+1)(x^m+3-1)

(Đúng nhớ like nhá !)

a) A xác định khi x\(\ne\)\(\pm\)2;x\(\ne\)1

b) A=\(\dfrac{\left(x+2\right)^2+\left(x-2\right)^2+16}{2\left(x-2\right)\left(x+2\right)}.\dfrac{x-2}{x-1}\)

=\(\dfrac{\left(2x^2+24\right)\left(x-2\right)}{2\left(x-2\right)\left(x+2\right)\left(x-1\right)}\)

=\(\dfrac{x^2+12}{\left(x+2\right)\left(x-1\right)}\)

c) A=\(\dfrac{x^2+12}{\left(x+2\right)\left(x-1\right)}\)=1

\(\Leftrightarrow\)x²+12=x²+x-2

\(\Leftrightarrow\)x=14

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a) (x+2y)²=x²+4xy+4y²

b) (x-3y)(x+3y)=x²-9y²

c) (5-x)²=25-10x+x²