# I'm veryconfused with an a level maths q

• liz
In summary, a triangle with sides that can be written in the form n^2+1, n^2-1, and 2n (where n>1) is right angled. This is proven by showing that the side n^2+1 is greater than or equal to the side 2n. However, the converse is false as shown by a counter example. The rest of the proof involves using Pythagoras' theorem, but the details are not fully understood.
liz
the question:
(im presuming n^2 means n squared)

prove the following result: "a traingle with sides that can be written in the form n^2+1, n^2-1, and 2n (where n>1) is right angled.
show, by means of a counter example, that the converse is false.

this q was taken from the back of the book "the curious incedent of the dog in the night-time" and there was a full proof but i don't understand some of it.

it start by exmplaining we need to prove which side is the longest by doing:

n^2+1 - 2n = (n-1)^2

if n>1 then (n-1)^2 >0

therefore n^2+1 > 2n

similarily (n^2+1) - (n^2-1) = 2

therefore n^2+1 > n^2-1

so n^2+1 > n^2-1.

the rest is worked out using pythagoras but then the converse bit has completely lost me.

if anyone would like to explain, then i would be very grateful. thanks!

He is simply showing which side is longer,

$$(n^2+1) - (2n) = (n-1)^2$$

The left hand side is the difference between 2 of the sides.

However, $(n-1)^2 \geq 0$

So you can replace $(n-1)^2$ with: $\geq 0$ and you get:

$$(n^2+1) - (2n) \geq 0$$

$$n^2+1 \geq 2n$$

So you know that the n2 + 1 side is greater or equal to the 2n side.

Please,do not double post.It's not really fair.

Daniel.

## 1. What is an A level maths question?

An A level maths question is a type of mathematical problem that is typically included in the curriculum for advanced level mathematics courses. It can cover a wide range of topics, including algebra, calculus, statistics, and more.

## 2. Why am I confused with an A level maths question?

Complexity and ambiguity are common characteristics of A level maths questions, which can make them challenging and confusing for students. Additionally, the pressure to perform well and the fear of making mistakes can also contribute to confusion.

## 3. How can I improve my understanding of A level maths questions?

One effective way to improve your understanding of A level maths questions is to practice regularly. This will help you become more familiar with different types of problems and develop problem-solving skills. You can also seek help from your teacher or a tutor if you need further clarification on certain topics.

## 4. What strategies can I use to tackle A level maths questions?

There are several strategies that can help you tackle A level maths questions more effectively. These include breaking down the problem into smaller, more manageable parts, using visual aids or diagrams to better understand the problem, and checking your work for mistakes.

## 5. How important is it to understand A level maths questions?

Understanding A level maths questions is crucial for success in this subject and for pursuing further studies or careers in fields that require strong mathematical skills. Additionally, improving your understanding of maths can also help develop critical thinking and problem-solving abilities that can be applied in other areas of life.

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