A TRICKY SAT radical equation | Can You Solve?

[@Segalmed]

Square it 4 times and get x^15 = 5^16 => x = 5^(16/15)

[@MrMartinSchou]

And what, exactly, did you square 4 times to end up at 15?

[@Segalmed]

@@MrMartinSchou each squaring removes one root and frees one x. But one has to be careful that those have to be included in the next squaring. 1. x*tripple SQRT 2. x^3 * double root 3. x^7 * single root 4. x^15 on the right side it's 5^2^2^2^2=5^16

[@haa4]

That’s the real root. I presume the other 14 are complex.

[@MarekLewandowski_EE]

We'd write the result as 5× (15)√5 (five times 15th root of five), the last reformulation being x^15 = 5^16 --> x^15 = 5^15 × 5 --> 15th root both sides, x = 5 × 5^(1/15) or 5× 15√5

[@DatBoi_TheGudBIAS]

notice that each x has an exponent that is half of the previous one and the first one is 1/2 so we have x^1/2 * x^1/4 * x^1/8 * x^1/16 = 5 sum exponents: x^(1/2+1/4+1/8+1/16) = 5 x^15/16 = 5 Therefore, x = 5^16/15

[@X00000370]

Very nice step-by-step explanation, your students must love your lectures.

[@astrolad293]

Expand from the inside out: x * sqrt(x) = x^(3/2) sqrt(x^(3/2))) = x^(3/4) x * x^(3/4) = x^(7/4)... Rinse and repeat until x^(15/16) = 5, so x = 5^(16/15)

[@prajval37]

This question was so easy

[@hugohabicht9957]

11 Minutes wasted 😂

[@milo351972]

thank you for reminding me of when we were in high school.

[@nemolai7989]

when I first saw the question my immediate reaction was that xsqrt(x) = 3/2, thus I used the second method, very nice video though

[@venkybabu4842]

99% of waves propogation is something like √2 under cube √2 under 4th√2 and so on. This equation is a special case of addition spectrum.

[@gillesandfio8440]

I got very close to the correct answer using the 2nd method in my head without use of pen and paper. Is easier.

[@에스피-z2g]

x^(1/2+1/4+1/8+1/16)=5 x^(15/16)=5 x=5^(16/15)

[@vladimirmitrovic2782]

x^[(1+2+4+8)/16]=5 x^(15/16)=5 x=5^(16/15)

[@yanssala2214]

X = 5^16. Por simple inspeccion

[@rv706]

More interesting question: solve for x>0 in *√(x√(x√(x√(x√(x√(x√(x....)))))))=5* , _where the dots extend indefinitely._ Solution: the function f(x) on the left hand side satisfies the functional equation √(xf(x))=f(x). Squaring and solving for f(x) gives that either f(x)=0 identically or f(x)=x identically. The first solution is incompatible with the equation. The second solution gives x=5.

[@kateknowles8055]

It also gives infinitely many complex solutions with magnitude 5. Are there some (infinity many ) arguments inbetween these infinitely many values on this circle? (Is Schroedinger's cat anywhere nearby? ) If so , please can we get an example or three?

[@Tat52]

X=5*5^(1/15) yes?

[@elsondeo]

How do we justify the de-nesting in second method?

[@quigonkenny]

√(x√(x√(x√x))) = 5 x√(x√(x√x)) = 5² --- ^2 x²(x√(x√x)) = 5⁴ --- ^2 x³√(x√x) = 5⁴ x⁶(x√x) = 5⁸ --- ^2 x⁷√x = 5⁸ x¹⁴(x) = 5¹⁶ --- ^2 x¹⁵ = 5¹⁶ = 5(5¹⁵) --- ¹⁵√ x = 5(¹⁵√5)

[@bbprintingshop8759]

1/7=1

[@uditjoshi5554]

I am not trying to be rude but both the methods are practicing same, just different way of representing lpl

[@ruchakhokale1852]

Both methods use different properties of exponents . It's not just about the representation of the answer is same . So both the method are practically different.......

[@uditjoshi5554]

@@ruchakhokale1852 generally when we talk about different methods to solve a question, we mean entirely different approach, i.e. using different concepts. Like some questions can be solved with quadratic formula, or spliting middle term, cooridinate geo and etc. While in this case, its practically the same way. As i said, just different way of writing

[@RealQinnMalloryu4]

(x ➖ 5x+5).

[@bebopalooblog2877]

It may be "simplified" but it's not actually solved. As always with simplifications, it's simply a restatement of the problem.

[@MarcoPolo-xu9te]

If X = 5^16/15, i guess we can simplify to x= 5√5, isn't it?

[@Tat52]

No. X=¹⁵√5^16=5* ¹⁵√5

[@milestones3005]

There are 15 solution

[@Coy33-co2tq]

No, there are infinite solutions, because we can add 1 or 2 or 3... until infinite and by both sides etc...

[@admiraloctavio5860]

@Coy33-co2tq??? No? There are 15 solutions because it’s a 15th order polynomial

[@Coy33-co2tq]

@admiraloctavio5860 I have solution 5^16/15

[@admiraloctavio5860]

@Coy33-co2tq I’m guessing you don’t have a maths background or are young. The fundamental theorem of algebra states that there are n complex solutions for an nth order polynomial. You only have one of the 15 solutions

[@I.R.S-r6y]

​@@admiraloctavio5860 Are you saying there are 15 ways to solve the math or are you saying there are 15 answers

[@Avalanchanime]

Me adding and multiplying exponents at the left: 🤡 Even tho it is ok... It is more complicated xD

[@cyruschang1904]

√(x√(x√(x√x))) = 5 x√(x√(x√x)) = 5^2 (x^3)(√(x√x)) = 5^4 (x^7)(√x)) = 5^8 x^(15) = 5^(16) x = 5^(16/15)

[@narindermultani2874]

Wrong answer because he forgot to square on both sides in the second step Please check it

[@فیروزاهنگری]

(x^15)^(1/16)=5 [(x^15)^(1/16)=5]^16 x^15=5^16 , x=5(5)^(1/15)

[@bbprintingshop8759]

Help me 1/7=1

[@kenhoo3702]

Too easy , x^1/2 = x^0.5 , x^(1 + 0.5) x^((1.5)/2) = x^0.75 , x^(1 + 0.75) x^(1.75/2)+ 1) = 5^3.75/2 x^(3.75/4) = 5 , this is it

[@richardbrookens2896]

Please talk a little faster so I have no chance of understanding you.

[@max-m5n]

Thank you.

[@025437359]

X=5¹⁶

[@darkshadow7938]

forgot it's x^15 and not x on the LHS

[@sudipchowdhury6075]

You american guys call it higher mathematics? 😂😂

[@KarmaCadet]

the channel's name is "higher mathematics", and I'm pretty sure that every american guy didn't create this channel

[@kateknowles8055]

How do you assume American? (I thought I was listening to a well educated Asian) ; "higher" is a comparative adjective, not superlative so no absolute claim is made in regard to the level of this mathematics.

[@glorymanheretosleep]

First method was a lot better and the easiest way to go through things.

[@Coy33-co2tq]

But I learned something from the second one about roots!!