Olympiad Mathematics | Learn how to solve the Radical Equation for X and Y | Math Olympiad Training

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Olympiad Mathematics | Learn how to solve the Radical Equation for X and Y | Math Olympiad Training

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[SuperYoonHo]

Aww thanks for these videos. I simply love them!















when will i get to be pinned?

[fevengr]

Somehow I missed the note that the solution had to be rational numbers, but when I realized that without that limitation there would be an infinite number of solutions, I looked again. After that it went pretty fast, not exactly the way you did it, but close. Clever problem! Thanks!

[philipkudrna]

Very Creative approach. I would also have started by squaring both sides, but the „splitting“ of the sum was already unorthodox and the „suppose x and y are the roots of a quadratic equation“ step was really genius. Would have liked to see a prove of the solution, though. Other than that once again: fantastic!

[sreeharieh]

Did the same thing. Except that i substituted y value with 3/4x and eventually factorised it by grouping. And found out both x and y

But the idea of considering x and y to be the roots of the equation and then forming the equation and factorising it is a very good approach to the answer

[Copernicusfreud]

I just used the quadratic formula after I split the one equation into the two equations of x + y = 2 and 2 * sq rt (x * y) = sq rt (3) which can simplify to y = 3/4x. plugging y = 3/4x into x + y = 2 simplifies to 4 x^2 - 8x + 3. Using the quadratic formula gives x = 3/2 and x = 1/2. Plugging x into the x + y = 2 equation, gives y = 1/2 and y = 3/2. (x, y) = (3/2, 1/2) or (x, y) = (1/2, 3/2). Thank you for the video.

[allahlover]

You are very very welcome.Thanks for these solutions

[Ramkabharosa]

√{a ± b√c} (where a, b, c are rational numbers) can be simplified to √x ± √y iff {a² - b².c} is the square of a positive rational number d. If there is no such d, the expression can't be simplified. In this example we have a=2, b=1, & c=3. So d = √{2² - 1².3} = √{4 - 3} = √1 = 1. So x = (2+1)/2 = 3/2 & y = (2-1)/2 = 1/2.

[anatoliy]

Oh, it`s very interesting way to solve the task trough a quadratic equation still at the start! I simply tried to solve it as a system of two equations X+Y=2 and XY=3/4 .... and notwithstanding I arrived at a quadratic equation ;))
Thank you so much for your nice math lesson, Mr PreMath! God bless you and your family!

[alster]

The splitting part is a bit tricky but the Vieta's Formula part made it easy

[luciferu.b.]

after determining x+y and xy, we could determine (x-y) and then solve for x&y

[davidfromstow]

Didn't have a clue - but I still enjoyed it - thank you!

[mathematicsolympiadchannel]

Sir thank you 😊 much for olympiad math.🙂🙂🙂

[xyz]

I started by working on the right side. 2 + sqrt3 = 3/2 + 1/2 + 2* sqrt(3/2) * sqrt(1/2)= (sqrt(3/2) + sqrt1/2)^2, thus sqrt x + sqrt y = (sqrt(3/2) + sqrt1/2), got the same results.

[nirupamasingh]

Vvvv nice question . Your way of explanation involving two three methods amazing.

[Deltachange]

We can do like in this way also
R.H.S= √2(2+√3)/2 (multiplying and dividing by 2)
√4+2√3/2
√(√3+1)^2/2.
√3+1/√2
√3/√2+√1/√2 (compare x and y)

[amnisharkawi]

Why you didn't pick:
X+y=root of 3.
2root xy=2.

Why did you supposed x and y roots for quadratic equation.

[fhfyhfyf]

How are we able to assume that x+y=2 and 2×✓xy=✓3
How is it possible to split the équation into two équations like that

[Mylorz]

It is an equation with two variables, so there are actuallly infinite solutions. If you put y=0 or x=0 you have different ones and so on.

[msafasharhan]

Hallo it s very diffcult to under stand is there another method how x+y=5 fro m wher z coming

[abiodunoseni]

Finally got the first question after attempting a series of premature questions