Áp dụng hệ thức Vi-ét cho phương trình `x^2 - 3x + 1 = 0:`

`x_1 + x_2 = 3`

`x_1 x_2 = 1`

Vì `x_1, x_2` là nghiệm nên:

`x_1^2 - 3x_1 + 1 = 0``to`` x_1^2 + 1 = 3x_1`

x_2^2 - 3x_2 + 1 = 0 to x_2^2 + 1 = 3x_2`

`x_1^2 - 3x_2 + 1 = (x_1^2 + 1) - 3x_2 = 3x_1 - 3x_2 = 3(x_1 - x_2)`

`x_1 \sqrt{x_1} = \sqrt{x_1^3}`
`7x_2 - x_1 = 7x_2 - (3 - x_2) = 8x_2 - 3`

Mà `x_2^2 - 3x_2 + 1 = 0 to = \frac{x_2^2+1}{x_2} = x_2 + \frac{1}{x_2}`

Nên `8x_2 - 3 = 8x_2 - (x_2 + x_1) = 7x_2 - x_1` (Cách này hơi dài, ta dùng cách khác)
Ta có `x_1, x_2 = \frac{3 \pm \sqrt{5}}{2}.` Vì `x_1 < x_2` nên:

`x_1 = \frac{3 - \sqrt{5}}{2}; x_2 = \frac{3 + \sqrt{5}}{2}`

`x_1 - x_2 = -\sqrt{5}`

Thay trực tiếp vào biểu thức:

Tử số: `3(x_1 - x_2) = -3\sqrt{5}`

Mẫu số: `x_1\sqrt{x_1} + \sqrt{7x_2 - x_1}`

`7x_2 - x_1 = 7(\frac{3+\sqrt{5}}{2}) - \frac{3-\sqrt{5}}{2} = \frac{21 + 7\sqrt{5} - 3 + \sqrt{5}}{2} = \frac{18 + 8\sqrt{5}}{2} = 9 + 4\sqrt{5} = (2 + \sqrt{5})^2`

`to \sqrt{7x_2 - x_1} = 2 + \sqrt{5}`

`x_1 = \frac{6-2\sqrt{5}}{4} = \frac{(\sqrt{5}-1)^2}{4} \Rightarrow \sqrt{x_1} = \frac{\sqrt{5}-1}{2}`

`x_1\sqrt{x_1} = \frac{3-\sqrt{5}}{2} \cdot \frac{\sqrt{5}-1}{2} = \frac{3\sqrt{5} - 3 - 5 + \sqrt{5}}{4} = \frac{4\sqrt{5}-8}{4} = \sqrt{5} - 2`

Mẫu số = `(\sqrt{5} - 2) + (2 + \sqrt{5}) = 2\sqrt{5}`

`A = \frac{-3\sqrt{5}}{2\sqrt{5}} = -1,5``

Đáp số: A `= -\frac{3}{2}`

opic 1: What you should or shouldn't do to become an ecotourist
To become a responsible ecotourist, there are several things we should and should not do:
What we should do:Travel responsibly: We should commute more on foot, by bicycle, or use public transport instead of cars to reduce emissions.
Conserve water and electricity: We should take quick showers instead of baths and remember to turn off the air-conditioners and lights when leaving our hotel rooms.
Support the local community: We should buy local products, eat local food, and respect their cultural traditions.

What we shouldn't do:Avoid excessive waste: We shouldn't use single-use plastics or buy products with too much packaging.
Protect wildlife: We shouldn't buy souvenirs made from endangered animal body parts (e.g., ivory, shells) or disturb animals in their natural habitats.
Do not litter: We shouldn't throw trash carelessly; instead, always put rubbish in the correct bins.

Topic 2: Some solutions to the problems of air pollution
Air pollution is a serious global issue, but we can reduce it by applying the following solutions:
Promote green transportation: People should walk, cycle, or use public transit like buses and trains more often to decrease exhaust fumes.
Use renewable energy: We should shift from fossil fuels (coal, oil) to clean energy sources like solar, wind, and hydro power.
Plant more trees: Planting trees and protecting forests are excellent ways to absorb carbon dioxide (\(\text{CO}_{2}\)) and release oxygen (\(\text{O}_{2}\)), making the air cleaner.
Stop burning waste: Encouraging recycling and banning the open burning of agricultural waste or household trash will significantly reduce smoke and toxic particles in the air.
Raise public awareness: Communities and schools should educate people on how to protect the environment and save energy daily.

Topic 3: Your favourite way to learn
Everyone has a unique learning style, but my favourite way to learn is interactive self-study combined with visual aids.
Why I prefer this way:High flexibility: Self-study allows me to manage my time efficiently and focus on topics that I am genuinely interested in.
Visual engagement: Using mind maps, educational videos (like on YouTube), and colorful charts helps me remember complex concepts much faster than reading long paragraphs.
Practical application: I love using online educational platforms like VietJack to solve practice tests and read clear explanations. This interactive method turns learning from a passive task into an active, enjoyable journey.

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