Video

Thank you

Can't you just make it ×^2(1-x)=80 x^2>0 => 1-x>0 -x=a a>0 80=x^2(a+1) 80=5.16 =>×^2=4,16 x=2,4 x=-4 a=4

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solved it very similarly

Are these videos for your class or just for utube?

Thanks, this was really helpful! You should definitely go into the field if you're this smart!

If you are watching this without searching like this.

Can be solved using log also right?

are ise asaan maine kar diya dimaa me hi i have solvd it in a verry very very short and easy method I study in class 12th but could have definately solved it because i made the trick to solve questions related to multiplication and powers in class 8th today evening I will post the video on it please see it mam by the wqay sorry if I sound rude but I believe that everybody should learn something new

I used only logarithms and fractions comparsion to solve it in a faster and clever way: ---------------------------------------------------------------------------------------------------------- 1) Transform the two numbers in natural logarithms: 50^50 = 50 ln(50) 49^51 = 51 ln(49) 2) Create a fraction with previous logarithms and separate it in two fractions: 50 ln(50) / [ 51 ln(49) ] --> --> ( 50 / 51 ) * [ ln(50) / ln(49) ] 3) Confront the first rational fraction and the second logarithmic fraction with the value 1: 50 / 51 < 1 ln(50) / ln(49) > 1 4) The absolute difference of numbers are always 1 (in this example): | 50 - 51 | = 1 | 49 - 50 | = 1 5) Because the natural logarithm function grows slower for every positive real number: ln(x) < x for any x € R+ ln(x+1) < (x +1) for any x € R+ 6) Now we can say that every fraction with numerator bigger that its denominator is always bigger that the same fraction with logarithmed numerator and denominator for any number greater that the constant e: (x +1) / x > ln(x + 1) / ln(x) for x > e x / (x +1) < ln(x) / [ ln(x +1) ] for x > e 7) That makes the confront at step 3 more accurate thanks to step 4: 51 / 50 > ln(51) / ln(50) --> 50 / 51 < ln(50) / ln(51) ln(50) / ln(49) is closer to 1 than 50 / 51 due to step 5 50 / 51 is more under the value 1 ln(50) / ln(49) is less up the number 1 8) Finally we can confront the initial fraction at step 2: ( 50 / 51 ) * [ ln(50) / ln(49) ] --> --> (a value more under 1) * (a value less up 1) = (a value under 1) --> --> ( 50 / 51 ) * [ ln(50) / ln(49) ] < 1 9) The fraction at step 2 has the denominator bigger that numerator due to being < 1: The numerator is 50 * ln(50) and the denominator is 51 * ln(49) Result: 49^51 > 50^50

Wow 😲😲 . I dont have that much patience finding em.

Amazing. Cheers from Portugal

"888^111 is greater OR EQUAL to 9^111" ? why not just ">"?

Could be solved mentally.

Решается в уме: ответ 2^36, 1 в любой степени = 1, вот и остается 2^6^2 -> 2 ^ 36 -> 64Гб, компьютерным языком.

Greetings. Thanks for sharing. You made a mistake in writing down the expression. You wrote Y^2 -2Y+8Y +16 instead of Y^2-2Y-8Y+16.

yawn already anseered forever. Please see black pen red pen for details on any a^b vs b^a as the base closest to e is the winner. We can know this for a fact without have to do much thinking based on the proof provided.

Vgud

V gud

222^333<>333^222 222^3<>333^2 a=log_222(333) 222^3<>222^(a2) 3<>a2 3/2<>a 3/2<>log_222(333) 3/2<>log_222(222)+log_222(3/2) Since: 1/2>log_222(3/2) so: 222^333>333^222

That's too complicated isn't it. 222^333 = 222^3 ^ 111 333^222 = 333^2 ^ 111 222^3 > 333^2 obviously or 111^3 * 2^3 (8) > 111^2 * 3^2 (9) obviously

V nice

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Keep it up. Waiting for next video😊

cool video make more videos like this about algebra😃

2,,,no paper needed

Can you not just set x^2 to n and solve the equation n^2 + n - 20 = 0?

sometimes your voice was destorted please fix it so that we can listen easily otherwise yu explained in detail.

very good examples

Please make video on explaining tenses as well.I am very weak.

after watching your video , i got whole thing

you explained this concept with so much details...thumbs up

Keep it up

That good knowledge for beginners to understand the basics Good effort

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Nice clickbate

Hello ! Please at 10''00' : -2a=1 (not -2a=a)

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5^7=125^8x 5^7=5^3×8x 5^7=5^24x 24x=7 X=7/24

Overall, the solution presented gets many things right, but it contains some clear flaws that one should be aware of. If one would judge your solution on a scale from 0-10, where 10 is entirely correct and 0 is entirely wrong I reckon that your solution deserves around 3 points. Probably not below 3, maybe 4 but definitely not 5 or above. We can begin by briefly mentioning the solution to the quadratic equation established at around the 3:30 mark in the video. The solution method is completely fine, although its execution is a bit lacking here; I'm mainly talking about the error at the 3:36 mark, where you write down the erroneous statement "-2+8=10", but using some arrows. Instead of writing "-2+8" as you did, you have to write either "-2-8" or "-(2+8)", since -2+8 is equal to 6 and nothing else; I want to be very explicit on this point in particular, as I see way too many students having similar confusion when handling minus signs. This is very important: if you want to break up the term -10y into separate terms, you can't abuse notation by writing -2y+8y, as this unambiguously means something that is different from what you're trying to convey. So learn to use parentheses properly, because this kind of error is not something that any competent mathematician wouldn't notice and remark upon. Another mistake comes up at around 7:30 in the video, where roots are cancelled after which one side suddenly has a plus/minus sign before it. While all the lines that have been written down here are individually correct on their own, the kind of reasoning they make up is flawed. The square root of a number is ALWAYS the positive one (or zero if we take the root of zero) if we work on the real number line, it's never anything else. So the implicit reasoning you use in this sequence is unclear. Why not just skip the root signs altoghether? They really add nothing of value except potential confusion. If you insist on having root signs, you could write "sin x=plus/minus root of (1/4)" instead. That way, there's absolutely no confusion as to what you're actually doing to arrive at your conclusion. This kind of expositional mistake is very common among students, and all it comes down to is practicing actually conveying mathematical reasoning in text form. This is something that hurts the quality of the video in general, and a very easy fix is to actually have some text in plain English that explains what reasoning is being used between steps. Students are for some reason very reluctant to do this, but it can serve to improve the overall quality and readability of a solution many times over. At around 8:00 in the video we come to a point which I personally dislike, and that is the use of the dreadful "sin^-1" notation for the inverse sine function. Since we often write "sin^k x" to denote (sin x)^k for any number k, the notation "sin^(-1)x" becomes ambiguous, as it's not always clear whether we're referring to the actual inverse sine function, or if we're referring to the reciprocal of sin x. This is somewhat mitigated in some countries where the secant and cosecant functions are widely used to denote the reciprocals of cosine and sine, respectively, but it's far better in my opinion to just use the notation "arcsin(x)" to avoid any confusion. Besides this, the line "x=sin^(-1)(plus/minus 0.5)" is actually incorrect, and this is something that has already been pointed out before in this comment section. This is because the inverse trigonometric functions (including arcsin) are functions, meaning that they will only have one output value for every valid input value. The equation "sin x= A", on the other hand, has an infinite amount of solutions, due to periodicity (and then there's the symmetry of the unit circle to take into account). So, writing sin x=A x=arcsin(A) is just wrong no matter what A is, unless the specified range for x is a subset of the interval [-pi/2,pi/2] (or [-90 degrees, 90 degrees] if we use degrees instead of radians). So, how should you actually write these lines down to get something that is correct? The answer is actually the same as in the previous paragraph: use plain English! It doesn't have to be much, but it can make the difference between clear and completely incomprehensible: "sin x=A. Thus, due to periodicity and symmetries in the unit circle, one gets that x= arcsin A+(n*360 degrees), OR x=180 degrees - arcsin A+(n*360 degrees)." Besides the use of plain English to convey my reasoning, note in particular the fact that we get two distinct cases. You didn't include the second case, which is why you didn't find all solutions to the equation. The final error I will remark upon is the one that occurs at around 10:30. I have yet to fully understand why this one happens at all, but it's something that I've observed briefly among students that are not used to university level mathematics. You write that sin x=plus/minus 0.866. This is wrong. Plain and simple. There is no reason whatsoever to replace the root of 3 divided by 2 with a decimal approximation; it does nothing to help the solution become more transparent, it's not correct, and no mathematician would ever recommend that you do it. Yet people do this kind of thing all the time, and I really don't get it. We tend to manage to bash out this kind of thinking from our first-year students at uni pretty quickly, but I'm not sure where the general idea comes from. It really makes no sense, and if there is one thing you should just stop doing, this is it. Use exact values throughout the entire solution, and if you want to give a decimal approximation you do that at the end when all relevant calculations that need the exact values are done. You should not take this comment as a complete roast of your work - as I wrote in the beginning, your solution gets many things right, including the key ideas to solving the problem. But rather, you should take this comment as a reminder that you still have a lot of room for improvement.

Fun Fact: 64 - 25 = 39

in squre equasina -b = x1+x2 c = x1*x2. obvious x1, x2 = 2, 8 en.wikipedia.org/wiki/Vieta%27s_formulas

Hi bro do u play pubg

sin = +- 1/2, then all the four values: 30, 150, 210 (-150) and 300 (-30) would work, not just +-30

Nice! Thanks. After the discovery of x=30 (first root); I could guess the other would be 60, since by symmetry the same logic would lead to cosx=1/2 hence x could also be 60.

-2+8=10

Writing 30 or 60 without the degree symbol is just not right. Also, what is the range of x? If x can be any real number, the correct answer for x should be n\pi+\pi/6, n\pi+pi/3, n\pi+2\pi/3,n\pi+5\pi/6 for any integer n.