Answer to Maths Olympiad Post

By -
In one of my earlier posts, I talked about the Maths Olympiad, a worldwide mathematics competition. I finished it off with an example Maths Olympiad problem from excellent.org. Here it is in its full glory.

If x and y are real numbers satisfying
            x2 + xy = 20 and y2 + xy = 30
what is the value of xy?

Today I’m back to answer this problem.
x² + xy = 20
y² + xy = 30
(x² + xy) + (y² + xy) = 50
(x² + xy) x (y² + xy) = 600
((x² + xy) x (y² + xy)) ÷ ((x² + xy) + (y² + xy)) = xy ∴
600 ÷ 50 = xy
             = 12

Yours in numbers, 
Lachlan

Comments

  1. Unknown20 October 2017 at 21:21

    ((x² + xy) + (y² + xy)) ÷ ((x² + xy) x (y² + xy)) = xy, that cannnot be if x and y are whole numbers.

    ReplyDelete
    Replies
    1. Unknown20 October 2017 at 21:33

      It is meant to be ((x² + xy) x (y² + xy)) ÷ ((x² + xy) + (y² + xy))=xy

      Delete
  2. Unknown20 October 2017 at 21:31

    Okay I understand this question now. It is a very good question! You should explain how the fifth step is equal to xy. It is very interesting.

    ReplyDelete

Post a Comment

Popular posts from this blog

Welcome

By -
Image
Hi, my name is Lachlan and I created this blog because I know that many of you out there are like me and just love maths. Many of you are probably parents thinking "My child loves maths, what should I do with them?!". Here you will be challenged and tested with a series of fun quizzes and tasks, and have your mind blown by astonishing facts and articles. You will also be introduced to a series of websites, videos and more, that will expand your knowledge of the vast world of math that we live in. However, in this blog we will also be diving into the depths of STEM, exploring not only pure math, but also the other areas of STEM, science, technology and engineering, which are all in turn related to math. My goal is that everybody reading my blog will take something out of it, whether it is a formula, or an idea of their own. I hope you enjoy. Yours in numbers, Lachlan P.S. I've kept all my old posts. See below. You can find our new bl...
Read more

the power of triangles

By -
Image
The triangle is the strongest shape, this is because if there is any pressure on top or beneath it the triangle will only bend in the section where there is the most pressure. With most other shapes - such as a circle or square - the top would just bend and then collapse on top of the rest of the structure. But at the same time triangles are not the stiffest shape but is actually pretty flexible compared to quite a lot of other shapes, which makes it one of the most important shapes for structures like bridges. You can try making a bridge out of straws and then see how strong it is!  Here are some bridges with triangles.                                                                                                   ...
Read more

Maths Olympiad

By -
Image
The Maths Olympiad is a world-wide competition, held at hundreds of locations around the globe. There are many Maths Olympiad competitions but some of the largest are the APSMO (Australasian Problem Solving Maths Olympiad) and of course the IMO (International Maths Olympiad). Not only is the Maths Olympiad a great competition to participate in, as I have three times so far, you can still learn from it even if you can’t participate. As an example, brilliant.org is an amazing website where you can practise Maths Olympiad questions without having to do the test. Here is one of their questions. Hopefully you’re up for the challenge.   If x  and y  are real numbers satisfying            x 2 + xy  = 20 and y 2 + xy  = 30   what is the value of xy ?   I’ll be back next with the answer in case you get stuck. Yours in numbers, Lachlan
Read more