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I got this question in my olympiad exam and i didn't know how to solve it : [2^(x-3)] × [3^(2x-8) ]=36 ; find x

By inspection : a²*(a-1)=18=3²*2 a=3

But you did not solve the problem. The problem was to "solve for x." 😀

At 1:06 you diverged from teaching them anything. You wrote 27-9 because you had rigged the problem to come out that way. You then dragged them through a bunch of rewriting that you could do only because you knew how the problem was going to end. Instead, you should have shown them the Rational Root Theorem and found a=3 as a root of the cubic. Then you should have shown them polynomial division and found a^2 + 2a + 6 as the other factor. Then you should have shown them how to complete the square and find a = -1+-sqrt(5) as the other two roots. What a pointless video.

Silly problem…. Right from the start you begin with 27-9 because obviously you’re looking for numbers that can be cubed and squared then subtracted and obviously 3^3-3^2=18 so we’re done because any moron can see that a = 3 by pattern. Done . Not sure of the point of this vid. Even to find your other solutions, just use synthetic division with the 3 that you find to reduce it to a quadratic equation which you could then solve for the other two solutions.

Soooooo...you already have to know the answer to get the answer...got it.

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If we see the Moon going westwards, but our maths calculation says otherwise, which one do we trust?

I am struggling with the idea that _-2+-2sqrt(2)i_ , when cubed, won't produce an _i_ thus making it not 36. (Wolfram says the flaw in my brain is that the squared part also produces _i_ ; I thought this would just become -1.)

and for everyone, If m is a range of real numbers, the answer is EXACTLY THE SAME See below : If f(m)=3^m-2^m-65, then it is a monotonically increasing function with f'(m)>0 We can get a rough idea of the range of m by computing f(2),f(3),f(4),..., even though it's not very detailed but when you find out that f(4)=0, it means that the only answer is 4 because f(m) is monotonically increasing function. However, in the realm of complex numbers, we can solve n^m=e^(mln(n))=x+yi, which has an infinite number of solutions due to periodicity.

you're wrong, because the question is that SOLVE FOR "X" non "m" 🤣🤣

The easiest way to simplify these nested square roots is to set them = a+sqrt(b). Then square both sides. Split the expression into a rational component and an irrational one, then solve as simultaneous equations.

Of course, since it is a multi choice question, it would be far better to note that 3 - 2√2 is about 0.2 so √(3 - 2√2) is about .44 ish Option A is about .7 option B is about .3 option C is about .41 Must be C. In a multi guess test SPEED is of the essence.

0.41421356237

this is definitely not grade 8 level

So it's a case of the Lambert - W function? Any way to solve it without using that function?

practically asmr math! i enjoyed the walkthrough of this problem but it would be helpful to have an explanation on the lambda w function

when you distribute your square to both the 5 and the root, you should show in red that the 5 is squared since you crossed out your outside square.

very cool!

I like your way better now I've seen it, but I went as follows: (11*5)^2 - (9*5)^2 (121*25) - (81*25) = 40*25 = 1000 Your way is better because it makes things easier when the numbers are harder to work with.

i got 7/32 idk what i did wrong

With the amount of lines you wrote, I thought you were going for the complex roots.

i din't get the second answer, but cool vid

0.5, by inspection. Possibly other solutions.

What about the complex solutions???

a=1

Instead of a long divide-and-conquer approach, a strategic surround-and-attack approach is much quicker What is known: the left 'a' term and the right 'a-1' term are not the same, their values must be equal, and the terms can differ by being positive and negative. What can produce the same values for 'a' and 'a-1'? 'O' won't do it. '1' won't do it. But right in between does it.

a - 1 = -a ; a = 1/2 . Much simpler!

Alternatively, you can take the fourth root and (for real numbers) add plus or minus on one side. This leads you directly to 2a-1=0

Why did this take so long to write out I got it in my brain in 30 seconds

7 × 8 × 9× 10 = 2×2×2×2×3×3×5×7= 1×2×3×4×5×6×7=7!

Are SATs difficult?

clearly , you could just calculate 10x9x8x7 , which is 5040 , which is equal to 7!

after the prime factorization step, don't you just look for the largest prime number for x? love this video

Nice problem! keep up the videos!

How many cups of coffee did he drink before filming this?

Go away.

bruh it is just 2^2048 = 2^2048 logically speaking

I just divided both sides by B to get 1+1+1 = B^2 then took the square root of both sides to get sqrt(3) = B

It looks tricky first but when you do it it feels easy😂

Entrance exam? For entry at 11?

Ngl beyond disappointed on how many steps you took 3b = b^3 3 = b^2 b = + sqrt(3); b = -sqrt(3);

3=b^(3-1) => 3=b^2 => b=+/-sqrt(3) and b=0

Zero

Simply divide both sides with b and get 3 = b squared => b = sqr(3).

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When I see this question, I instantly know m= 4, because 2^4 is 16, 3^4 is 81, 3^3 is 27, power 3^m grows much faster than 2^m, so it just has to be 4, not even trial and error just intuition.

You've only found one possoble solution. If you had chosen 1x65, you would have gotten a different answer.

Not sure how this method is any different to just using trial and error. You've assumed that m is an integer for the part where you trial and error guess that (x-y)=5, (x+y)=13. For an equation of this type it would be much quicker to just guess values of m from the start.

43rd view, 2nd like, 1st comment: Please increase the audio volume in future videos, because in every other respect this is a brilliant video