Olympiad Math | Learn How to Find the Value of x^(1/2)+1/x^(1/2) Quickly | Math Olympiad Training

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Olympiad Math | Learn How to Find the Value of x^(1/2)+1/x^(1/2) Quickly | Math Olympiad Training
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[ishitamondal]

Wow nice ❤️
Thanks a lot
Lots of love from India

[tggtgg]

Dear Sir, I appreciate your effort to show math is easy and simple. But, be careful no to mislead students that are not able to identify the mistakes(for example SHuhua accepted your answer as it is). This solution must be 4, not -4. X the value of x is given positive initially, the square root of positive number is positive, the sum of two positive numbers is positive. In addition x cannot be negative as the negative numbers do not have square root.

[abdulrahmani.aljuraid]

sqr(x) is positive and sqrt(1/x) is also positive, so the sum is positive and equal to 4

[MrLeith]

Hi Sir and thank you for all your posts.
Another way to handle this expression is to notice that x = 7 + 4sqrt(3) = ( 2 + sqrt(3))².
Then sqrt(x)=2+sqrt(3) and 1/sqrt(x) = 2-sqrt(3)

[lybcxds]

تمرين جيد . شكرا جزيلا لكم والله يحفظكم ويرعاكم ويحميكم . تحياتنا لكم من غزة فلسطين

[mainuddinahmed]

Dear Sir, I appreciate your videos. But I think, here is a problem/mistake. We should know √x means non negative square root of x. Here √x and 1/√x both are positive. So the answer is 4 only.

[govindashit]

Simple.
Positive "4" is right answer.
Thanks sir.

[math]

love this Olympiad question, your solution was very well explained

[rorydaulton]

Your final expression has the square root of x twice. This is the *principal* square root, which is necessarily non-negative. Thus the final answer must be non-negative, and the only answer is 4, not -4.

[Postoronnim-VV]

Здесь все просто. 7+4sqrt(3) =(2+sqrt(3))^2
Подставляем это значение вместо "х" и находим решение 4
Only positive 4

[xyz]

I did it by getting the value of sqrt(x) from x = 7 + 4 sqrt(3) = 3 + 4 + 4 sqrt(3) = (2 + sqrt(3) ) ^2 hence sqrt(x) = 2 + sqrt(3) put the value in and rationalize…

[om]

i think only 4 is the correct answer becoz according to AM GM inequality the exp is always greater than or equal to 2 hence -4 is rejected

[HappyFamilyOnline]

Very well explained👍
Thank you so much for sharing😊

[outofthebots]

I got same answer but used a different solution.
x = 7 + 4sqr(3) can be written as x = (sqr(3) + 2)^2
so sqr(x) = sqr(3) + 2
so 1/sqr(x) = 1/(sqr(3) + 2) if we multiply by (2 - sqr(3))/(2 - sqr(3))
so 1/sqr(x) = 2 - sqr(3)
so then sqr(x) - 1/sqr(x) = sqr(3) + 2 + 2 - sqr(3) = 4

[luffiz]

the sum of two positive numbers is positive.
answer: 4

[anatoliy]

My old math teacher used to say: simplify - half solve! It seems that you also apply this rule :)) Thank you very much, Professor! All the best to you! Be happy!

[prabhudasmandal]

My approach is 7+4√3 is (2+√3)^2, so, √x=+/_(2+√3).now simplifying the expression( √x+1/√x) we get(x+1)/√x.putting the values of x and √x we get the result as(7+4√3+1)/(2+√3)+-.or (8+4√3)/do or4(2+√3)/+-(2+√3)=+/-4 ans.

[bharatsrivastava]

For real solution, we know that the domain of √x is always greater or equal to zero. But here √x is in denominator, so the domain of √x is always greater than zero. So, the value of √x + 1/√x will always positive and hence -4 is rejected.

[gordonspond]

6:20 Shouldn't the result just be +4? Inspection of the question shows that we are adding to positive numbers, so I don't see how the result could be negative.

[RaphaelTrujillo]

Los pasos para la solución:

1. x = 7 + 4 * sqrt(3) = 4 + 4 * sqrt(3) + 3 = (2 + sqrt(3))^2
2. sqrt(x) = 2 + sqrt(3)
3. sqrt(x) + 1/sqrt(x) = (2 + sqrt(3)) + 1/(2 + sqrt(3)) = (2 + sqrt(3)) + (2 - sqrt(3)) = 4

En el paso 1 hay un binomio cuadrado perfecto
En el paso 3 se multiplico por la conjugara (2 - sqrt(3)) para hacer diferencia de cuadrados
(2 + sqrt(3))*(2 - sqrt(3)) = 4 - 3 = 1