xác định nghĩa tương minh và nghĩa hàm ẩn trong câu:"mảnh giấy làm nên thân giáp bảng/nét son điểm rõ mặt văn khôi"
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Lời giải:
** Sửa đề: $A=\frac{ab}{(b-c)(c-a)}+\frac{bc}{(c-a)(a-b)}+\frac{ac}{(a-b)(b-c)}$
\(A=\frac{ab(a-b)+bc(b-c)+ac(c-a)}{(a-b)(b-c)(c-a)}=\frac{(a^2b+b^2c+c^2a)-(ab^2+bc^2+ca^2)}{-[(a^2b+b^2c+c^2a)-(ab^2+bc^2+ca^2)]}=-1\)
Lời giải:
$5x^2+5y^2+8xy-2x+2y+2=0$
$\Leftrightarrow 4(x^2+y^2+2xy)+(x^2-2x+1)+(y^2+2y+1)=0$
$\Leftrightarrow 4(x+y)^2+(x-1)^2+(y+1)^2=0$
Ta thấy: $(x+y)^2\geq 0; (x-1)^2\geq 0; (y+1)^2\geq 0$ với mọi $x,y$
Do đó để tổng của chúng bằng $0$ thì:
$(x+y)^2=(x-1)^2=(y+1)^2=0$
$\Rightarrow x=1; y=-1$
Khi đó:
$M=0^2+(1-2)^{2024}+(-1+1)^{2025}=0+1+0=1$
N = x² - 2xy + 3y² - 4y + 2023
= (x² - 2xy + y²) + (2y² - 4y) + 2023
= (x - y)² + 2(y² - 2y + 1) + 2021
= (x - y)² + 2(y - 1)² + 2021
Do (x - y)² ≥ 0 với mọi x, y ∈ R
⇒ (y - 1)² ≥ 0 với mọi y ∈ R
⇒ (x - y)² + 2(y - 1)² ≥ 0 với mọi x, y ∈ R
⇒ (x - y)² + 2(y - 1)² + 2021 > 0 với mọi x, y ∈ R
Vậy N luôn dương với mọi x, y ∈ R
71. A. light B. slight C. lightly D. lighted
72. A. possible B. capable C. probable D. likely
73. A. continued B. chased C. followed D. taken
74. A. each one B. one other C. one the other D. one another
75. A. relation B. relationship C. relation D. relatives
76. A. younger B. most young C. youngest D. young
77. A. easy B. basic C. fundamentally D. elementary
78. A. changed B. transferred C. reserved D. exchanged
79. A. sense B. sensation C. sensitivity D. sensible
80. A. inactive B. inaccurate C. inappropriate D. inexact
61. Who brought the legend of Santa Claus to the USA according to the passage?
A. Sinter Klaas B. Saint Nicholas C. A German D. Dutch settlers
62. Santa Claus was traditionally described as a________.
A. tall man who could walk through the air. B. fat, jolly, old man.
C. religious figure. D. fat man riding a white horse.
63. Santa Claus in North America was depicted as________.
A. a man with the strict disciplinarian character of Black Peter.
B. a good old man with less religious character.
C. one with religious attributes of Saint Nicholas.
D. a jolly man on horseback.
64. Who was Black Peter?
A. an elf accompanying Saint Nicholas. B. an elf who rode a white horse.
C. one of the disobedient children. D. a popular traditional figure.
65. What word is closest in meaning to “attributes”?
A. symbols of a person B. natural qualities C. effects D. outer appearance
66. Where did the legend of Santa Claus come from?
A. the North Pole B. Europe C. North America D. the City of New York
67. 1823 was mentioned as a year when________.
A. Clement Clark Moore wrote his first poem
B. Clement Clark Moore’s poem made him popular
C. Saint Nicholas visited New York
D. the image of Santa Claus was transformed
68. According to Clement Clark Moore’s poem
A. Santa Claus had nothing different in appearance from the traditional one.
B. Santa Claus had wings and could fly.
C. Santa Claus liked poetry.
D. Santa Claus was a kindly saint who flew over housetops in a sleigh.
69. The answer “Yes, Virginia, there is a Santa Claus” is an illustration for the fact that________.
A. the New York Sun was popular with children.
B. Santa Claus was a prominent figure at that time.
C. newspapers are unreliable.
D. Virginia O’Hanlon was a reader of the New York Sun
70. Which of the following statements is TRUE?
A. Santa Claus was an imaginary old man created by artists based on traditional figures.
B. Living in the North Pole, Santa Claus visited children at Christmas.
C. Santa Claus was a real figure living in northern America.
D. Santa Claus was a story based on Saint Nicholas and Black Peter.
51. What is the author's main purpose in writing this passage?
A. To trace the career of Arnold Guyot.
B. To describe feature of the undersea world.
C. To present the results of recent geologic research.
D. To discuss underwater ridges and volcano chains
52. The word “conceal” is closest in meaning to which of the following?
A. Contain B. Erode C. Hide D. Create
53. The passage implies that guyots were first detected by means of________.
A. a fathometer B. computer analysic
C. a deep-sea diving expedition D. research submarines
54. The author indicates that Arnold Guyot________.
A. was Harry Hess's instructor B. invented the fathometer
C. named the guyed after himself D. taught at Princeton University
55. What does the passage say about the Arctic Ocean?
A. The first guyot was discovered there.
B. No guyots have ever been found there.
C. There are more guyots there than in any other ocean.
D. It is impossible that guyots were ever formed there.
56. The author states that offshore canyons and guyots have which of the following characteristics in common?
A. Both are found on the ocean floor near continental shelves.
B. Both present oceanographers with a mystery.
C. Both were formed by volcanic activity.
D. Both were, at one time, above the surface of the sea.
57. According to the passage, most guyots are found at a depth of________.
A. less than 600 feet. B. between 600 and 3,200 feet.
C. between 3,200 and 6,500 feet D. more than 8,200 feet
51. Which of the following is closest in meaning to the word “rubble”?
A. Fragments B. Mixture C. Columns D. Core
51. According to the passage, which of the following two processes were involved in the submersion of guyots?
A. Erosion and volcanic activity.
B. The sinking of the sea floor and the rising of sea level.
C. Mountain building and the action of ocean currents
D. High tides and earthquakes
60. According to the passage, when did sea level significantly rise?
A. In 1946 B. In the nineteenth century
C. From 8,000 to 11,000 years D. 80 million years ago