Mathematical Challenge| Learn how to Solve Exponential Radical Equation | Math Olympiad Training

Can you solve the given exponential radical equation for x?

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Mathematical Challenge| Learn how to Solve Exponential Radical Equation | Math Olympiad Training

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[ishitamondal]

Thanks a lot sir ....
It was way more helpful ....
These videos are literally enhancing my capability to solve problems ..

[diamonddudeygo]

I just squared each side to get 888^sqrt(x) = 888^(2/sqrt(x)), then equaled the exponents to get sqrt(x) = 2/sqrt(x) and moved the denominator in the right hand side to the left hand side to get x=2.

[montynorth]

Square both sides.
888^root x = 888^(2/root x) (numerator multiplied by 2 for squaring)
root x = 2/root x.
2 = (root x)^2
2 = x.

[nirupamasingh]

V intelligent question vnice explanation

[mathshelper]

Thanks sir.If possible then make videos about how to get the approach in a question👍

[HappyFamilyOnline]

Very helpful video👍
Thank you so much for sharing🎉

[tugrulhankabalgeometry]

your videos are good but if you add more geometry it would be great

[math]

the solution was very well demonstrated, excellent presentation

[ganeshdas]

On squaring both sides the expression becomes
888^✓x = (888)^x
✓x = x
x^2 = x ( on squaring again)
x(x - 1) = 0
x =0 and x=1, both values satisfy the given expression.

[l.w.paradis]

This reasoning shows why you can substitute any positive integer n for 888; x will always equal 2.

n = 888 just makes it look weird in a good way. :)

[Waldlaeufer]

I would tend to say that x = 2 is the solution. Now let's watch the video...

[christopherellis]

It couldn't have been anything else?

[fevengr]

Having a square root term in the exponent looked potentially complicated so I substituted P for SQRT(X). Although that turned out to be an unnecessary additional step, I did manage to get the correct answer. It’s interesting that you choose a mixture of hard and easy problems. It keeps me coming back for more. Thanks!

[KataisTrash]

I had an alternate approach while trying so solve it: When you have 888^(sqrt(x)/2)=888^(1/sqrt(x)), you can rise both sides to sqrt(x), which when simplified will result in 888^(x/2)=888^1, and now you can solve x/2=1. I found this approach a bit more intuitive, since raising to sqrt(x) removes sqrt(x) from the whole equation to begin with, in this case. But yeah obviously cross-multiplying works even better, it just wasn't the first thing that came to mind for me.

[anatoliy]

Radical equations are as interesting as exponential ones, especially both in one! I`ve solved it accurate in the same way that you. Thank you so much for a math lesson and for a spoken English one as well, sir! All the best to you! Greetings from Ukraine<))

[chaparral]

the funny thing is that 888 has nothing to do with the solution. Could be any positive number. I know a funny integral excercise which uses the same trap.
Calculate the integral with the boundaries from 1/1000 to 1000 of function 1/x *sin(x - 1/x)

[devondevon]

Answer x=2
sqrt (888^sqrtx)= 888^1/sqrt x
888^sqrt x = 888^2/sqrt x square both sides
sqrt x = 2/sqrtx relating the base
(sqrt x)(sqrt x) =2
x=2

[haroldwood]

Thank you! I am far from being mathematically gifted, but your clear instructions open a little window into that world for me.

[alster]

Wow!

It may look hard at first, but it is very easy to solve

[davidfromstow]

Very simple and obvious - but only sfter you have shown the right way to solve it!