Đặt \(a=\sqrt[3]{3+\sqrt{9+\frac{125}{27}}},b=\sqrt[3]{-3+\sqrt{9+\frac{125}{27}}}\to a^3-b^3=6,ab=\sqrt[3]{\frac{125}{27}}=\frac{5}{3}.\)

Từ đây với \(S=a-b\to S^3=a^3-3ab\left(a-b\right)-b^3=6-5S\to S^3+5S-6=0\)

Suy ra \(\left(S-1\right)\left(S^2+S+6\right)=0\to S=1\to S\) là số nguyên.

E=\(\dfrac{15}{11.14}+\dfrac{15}{14.17}+\dfrac{15}{17.20}+...+\dfrac{15}{74.77}\)

E=5(\(\dfrac{3}{11.14}+\dfrac{3}{14.17}+\dfrac{3}{17.20}+...+\dfrac{3}{74.77}\))

E=5(\(\dfrac{1}{11}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{20}+...+\dfrac{1}{74}-\dfrac{1}{77}\))

E=5(\(\dfrac{1}{11}-\dfrac{1}{77}\))=5.\(\dfrac{6}{77}\)

E=\(\dfrac{30}{77}\)

A=(2+2²)+(2³+2⁴)+...+(2⁹+2¹⁰)

=2(1+2)+2³(1+2)+...+2⁹(1+2)

=2.3+2³.3+...+2⁹.3

=3.(2+2³+...+2⁹) luôn chia hết cho 3

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 following questions.

One of the highest honors for formalists, writers, and musical composers is the Pulitzer Prize. First awarded in 1927, the Pulitzer Prize has been won by Ernest Hemingway, Harper Lee, John F. Kennedy, and Rodgers and Hammerstein, among others. As with many famous awards, this prize was named after its founder, Joseph Pulitzer.

Joseph Pulitzer’s story, like that of many immigrants to the United States, is one of hardship, hard work and triumph. Born in Hungary, Joseph Pulitzer moved to United States in 1864. He wanted to be a reporter, but he started his American life by fighting in the American Civil War. After the war, Pulitzer worked for the German - language newspaper, the Westliche Post. His skills as a reporter were wonderful, and he soon became a partial owner of the paper.

In 1978, Pulitzer was able to start a newspaper of his own. Right from the first edition, the newspaper took a controversial approach to new. Pulitzer wanted to appeal to the average reader, so he produced exciting stories of scandal and intrigue. Such an approach is commonplace today, but in Pulitzer’s time it was new and different. The approach led to the discovery of many instances of corruption by influential people. Pulitzer ‘paper became very famous and is still produced today.

The success of Joseph Pulitzer’s newspaper made him a very wealthy man, so he wanted to give something back to his profession. Throughout his later years, he worked to establish university programs for the teaching of journalism, and he funded numerous scholarships to assist journalism students. Finally, he wanted to leave a legacy that would encourage writers to remember the importance of quality. On his death, he gave two million dollars to Columbia University so they could award prizes to great writers.

The Pulitzer Prize recipients are a very select group. For most, winning a Pulitzer Prize is the highlight of their career. If an author, journalist, or composer you know has won a Pulitzer Prize, you can be sure they are at the top of their profession.

Which sentence about Joseph Pulitzer is NOT true according to the reading passage?

A. Joseph Pulitzer was the first writer to the win the prize in 1917

B. The prize is aimed at encouraging a writer’s career

C. Joseph Pulitzer left money to award to the prizewinners

D. Receiving the prize is one of the highest honors for writers