\(x^3+px^2+\left(p-1+\frac{1}{p-1}\right)x+1=0\)

\(\Leftrightarrow\left[x-\left(1-p\right)\right]\left[\left(p-1\right)x^2+\left(p-1\right)x+1\right]=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=1-p\\\left(p-1\right)x^2+\left(p-1\right)x+1=0\end{cases}}\left(1\right)\)

Để pt có no duy nhất <=> hệ pt (1) có no duy nhất

<=> pt(1) vô no hoặc pt(1) có nghiệm kép x₁=x₂=1-p

Kết hợp điều kiện \(p>1,p\inℕ\)ta tìm được các giá trị của p thỏa mãn là

p=2,3,4

\(x^3+px^2+\left(p-1+\frac{1}{p-1}\right)x+1=0\)

\(\Leftrightarrow\left(p-1\right)x^3+p\left(p-1\right)x^2+\left(p^2-2p+2\right)x+p-1=0\)

\(\Leftrightarrow\left(x+p-1\right)\left[x^2\left(p-1\right)+x\left(p-1\right)+1\right]=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=1-p\\x^2\left(p-1\right)+x\left(p-1\right)+1=0\left(1\right)\end{cases}}\)

Phương trình có nghiệm duy nhất khi phương trình \(\left(1\right)\)vô nghiệm hoặc có nghiệm kép bằng \(1-p\). 

- \(\left(1\right)\)vô nghiệm: 

\(\Delta< 0\Leftrightarrow\left(p-1\right)^2-4\left(p-1\right)< 0\Leftrightarrow1< p< 5\).

- \(\left(1\right)\)có nghiệm kép bằng \(1-p\).

\(\left(1\right)\)có nghiệm bằng \(1-p\)suy ra \(\left(1-p\right)^2\left(p-1\right)+\left(1-p\right)\left(p-1\right)+1=0\)

mà \(p>1\)nên phương trình này vô nghiệm. 

Vậy \(1< p< 5\)mà \(p\)nguyên nên \(p\in\left\{2;3;4\right\}\).

Rules of Subject-Verb Agreement:

Rule 1:

Singular subjects need singular verbs, while plural subjects require plural verbs. ‘Be’ verbs change the most according to the number and person of the subject.  Other verbs do not change much on the basis of the subjects except the verbs of the simple present tense. If the subjects are a third person singular number, the verbs are used with s/es when they are in simple present tense. The verbs with s/es in the sentence are called singular verbs.

‘Be’ verbs according to number and person of the subject.

 Example: 

Rule 2:

When the prepositional phrases separate the subjects from the verbs, they have no effect on the verbs.

Example:

A study (singular subject) on African countries shows (singular verb)  that 80% of the people (plural subject) of this continent live (plural verb) below the poverty line.

The perspective of different people varies from time to time.

The fear of terrorists and militants has made them flee the city.

Rule 3:

Nouns connected by the conjunction and in the subject work as the plural subject and take a plural verb.

Example:

• Alex and Murphy are coming here.
• Robin and his friends want to go on a tour.
• Apples and mangoes are my favorite fruits.

Rule 4:

If the conjunction ‘and’  is replaced by together with/ along with/ accompanied by/ as well as, the verb will have no effect for the later part of these expressions. The words prior to these expressions are the subjects.

Example:

• Tom, along with his brothers is going to the city. (‘His brothers’ is not the subject of this sentence.)
• Alex, as well as his parents, is coming to the party.
• The boys, accompanied by their teacher Mr. Robbins are planning a tour.

Note: If these expressions are replaced by ‘and’, the subjects will be regarded as plurals, and so the verbs have to be plural.

Example: Tom and his brothers are going to the city.

Rule 5:

Some nouns are always singular and indefinite. When these nouns become the subjects, they always take singular verbs.

*Note:  Either and neither are singular if they are not used with or and nor.

Example:

• Everybody wants to live happily.
• Something is bothering him.
• No human being lives in that house.
• Neither of you is responsible enough to handle it.
• Each student has to submit a separate assignment.

Rule 6:

Some nouns are always plural. These nouns have two parts.

Example:

• My pants are in the drawer.
• Your eyeglasses are dirty.
• These scissors are useless.

Note: If these words are preceded by the phrase a pair of, they will be regarded as singular subjects.

Example:

• A pair of pants is needed.
• This pair of trousers is ugly.

Rule 7:

None is a singular subject when it is used alone. When it is used with a prepositional phrase starting with of, the subject can be both plural and singular.

Example:

• None of the money has been used.
• None of the teacher wants failure for students.
• None of the students want to fail.
• None of the bottles are clean enough to keep water.

Note: No + plural noun takes plural verbs.

Example: no men are hungry now.  

Rule 8:

Either . . .  or, neither . . . nor, or, and nor take two nouns before and after them. The nouns placed after these conjunctions are regarded as the subjects of the sentence. The nouns placed prior to the words or and nor have no effect on the verbs.

Example:

• Neither Alex nor his brothers are going to the party.
• Either John and Alex or I am doing it.
• I or Robert opens the door when someone comes.
• Neither the boys nor we are responsible for it.

Rule 9:

The sentences beginning with here/there are different in structure. In this case, the subject comes after the verb.

Example:

• Here comes(verb) the lion(subject).
• There is a pond near the house.
• There are some candies on the table.
• Here is the document for your car.

Rule 10:

Collective nouns are usually regarded as singular subjects.

Examples:

Twenty dollars is not a lot of money. (Here, the noun is plural, but the subject is regarded as a collective noun.)

Note:  The following phrases are also regarded as collective nouns and thus singular subjects.

Example:

A flock of sheep always moves together.

Rule 11:

A number of + noun is a plural subject, and it takes a plural verb. The number of + noun is a singular subject, and it takes a singular verb.

Example:

A number of dancers are coming to the party. (Indefinite number of dancers – plural)

Rule 12:

If a gerund or an infinitive comes as a subject, the verb will always be singular.

Example:

Swimming is a good exercise.

Rule 13:

 If the + an adjective appears as the subject of a sentence, it will be plural.

Example:

The pious are loved by God.

* tham khảo mạng *

tin học lớp 4/5 có hết

Bước 1: Các bạn mở trang web muốn lưu lại sau đó nhấn Ctrl + A để bôi đen toàn bộ trang web hoặc dùng chuột bôi đen phần nội dung mà bạn muốn lưu lại.

Bước 2: Sau khi bôi đen xong các bạn nhấn Ctrl + C để copy phần đã bôi đen.Tiếp theo đó bạn mở Word và nhấn Ctrl + V để dán nội dung của trang web vào Word, nếu có thông báo hiện lên các bạn nhấn Yes.

\(A=\frac{1+sin4x-cos4x}{1+sin4x+cos4x}=\frac{sin4x+\left(1-cos4x\right)}{sin4x+\left(1+cos4x\right)}=\frac{sin4x+2sin^22x}{sin4x+2cos^22x}=\frac{2sin2x\left(cos2x+sin2x\right)}{2cos2x\left(sin2x+cos2x\right)}\)

\(=\frac{2sin2x}{2cos2x}=tan2x\)

\(\frac{tan2x-tanx}{tan2xtanx}=\frac{1}{tanx}-\frac{1}{tan2x}=\frac{1}{tanx}-\frac{1-tan^2x}{2tanx}=\frac{1+tan^2x}{2tanx}=\frac{1+\frac{sin^2x}{cos^2x}}{\frac{2sinx}{cosx}}\)

\(=\frac{1}{2cosxsinx}=\frac{1}{sin2x}\)

suy ra \(\frac{tan2xtanx}{tan2x-tanx}=sin2x\).

a-b=a+b

Trả lời :

a - b = -a + b

~HT~

Của mk ms đúng

a) Chú ý rằng với hai người \(A\)và \(B\)thi đấu với nhau thì \(A\)thi đấu với \(B\)và \(B\)thi đấu với \(A\).

Mỗi người sẽ đấu với \(n-1\)người, nên tổng số ván đấu của giải là: 

\(\frac{n\left(n-1\right)}{2}\).

b) Giả sử \(n=12\).

Tổng số ván đấu của giải là: \(\frac{12.11}{2}=66\).

Tổng số điểm của tất cả các kì thủ là: \(2\times66=132\).

Kì thủ cuối thắng ba kì thủ đứng đầu, do đó số điểm kì thủ cuối ít nhất là \(2.3=6\).

Do số điểm các kì thủ đôi một khác nhau nên tổng số điểm tối thiểu của tất cả các kì thủ là: 

\(6+7+8+9+10+11+12+13+14+15+16+17=138>132\).

Do đó không thể xảy ra điều này. 

Ta có đpcm. 

Mới học lớp 3ko biết❌👎🥶♨️📵❌❌🆘