\(\cos\left(\frac{\pi}{6}\left(4x+\sqrt{10+x^2}\right)\right)=-\frac{\sqrt{3}}{2}\)

\(\cos\left(\frac{\pi}{6}\left(4x+\sqrt{10+x^2}\right)\right)=\cos\left(\frac{5\pi}{6}\right)\)

\(\frac{\pi}{6}\left(4x+\sqrt{10+x^2}\right)=\frac{5\pi}{6}\)

\(4x+\sqrt{10+x^2}=5\)

\(\sqrt{10+x^2}=5-4x\)

\(10+x^2=25-40x+16x^2\)

\(15-40x+15x^2=0\)

\(\sqrt{\Delta}=10\sqrt{7}\)

\(\orbr{\begin{cases}x_1=\frac{40+10\sqrt{7}}{30}=\frac{4+\sqrt{7}}{3}\left(ktm\right)\\x_2=\frac{40-10\sqrt{7}}{30}=\frac{4-\sqrt{7}}{3}\left(tm\right)\end{cases}}\)

vậy pt có n⁰ duy nhất là \(\frac{4-\sqrt{7}}{3}\)

????????????? nhs riêng cho thầy cô chứ 

Cái này phải hỏi riêng Thầy, Cô chứ sao lại đăng lên đây

1, ▲ Trích mẫu thử vào từng ống nghiệm đánh dấu từ 1 đến 4

    ▲ Chọn quỳ tím làm thuốc thử ta được:

        + Dung dịch làm quỳ tím chuyển đỏ : HCl

        + Dung dịch làm quỳ tím chuyển xanh : NaOH và Na₂CO₃

        + Dung dịch làm quỳ tím không đổi màu : MgCl₂

    ▲ Dùng HCl đã nhận biết làm thuốc thử để phân biệt NaOH và Na₂CO₃

        + Dung dịch tạo khí sủi bọt : Na₂CO₃

        + Dung dịch không tạo chất khí là : NaOH

2, ▲ Trích mẫu thử vào từng ống nghiệm đánh dấu từ 1 đến 4

    ▲ Chọn quỳ tím làm thuốc thử ta được:

         +  Dung dịch làm quỳ tím hóa đỏ : HCl và H₂SO₄ 

          + Dung dịch làm quỳ tím hóa xanh là : Na₂CO₃ 

         + Dung dịch không đổi màu quỳ tím : BaCl₂

   ▲ Dùng BaCl₂  đã phân biệt được để phân biệt HCl và H₂SO₄ ta được:

         + Dung dịch tác dụng được với H₂SO₄ tạo thành chất kết tủa là H₂SO₄

          + Còn lại là HCl

có màu da cam nha bn !!!!

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

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

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

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 *