Can You Solve This? (Probably Not...)

😎 Become a member to have exclusive access:

🔔 Subscribe:

🥹 Consider supporting us on Patreon:

[thedude]

I wonder why we didn't apply the analysis on the first proof, just before multiplying by x. The analysis is done by distinguishing the cases x>=0 or x<0.

You just need to swap the inequality direction when multiplying both sides by a negative number.

Something which I would also point out is that we capture all and only proper solutions despite cubing because the function f(x)=x^3 is strictly monotone. This means that a>b <=> a^3 > b^3. This would not work with squaring!

[Sergonizer]

0:36 instead, move -7 to the left side. (1+7x)/x≥0. This clearly leads to two solutions, one is both top and bottom being non-negative and one is both top and bottom being non-positive. So x≠0 && (x ≥ 0 && x ≥ -1/7 || x ≤ 0 && x ≤ -1/7), meaning x > 0 or x ≤ -1/7.

[benjaminvatovez]

Thank you for the video. I think we could make it simple this way: after cubing the two members of the inequation (we can do it with no risk as the power is odd), we can just write (1/x)-1>=-8 then (1/x)+7>=0 then (7x+1)/x>=0 The solution can be obtained quickly using a sign table.

[SobTim-euxu]

Great video!)
I love symbols in this video!)
And idea for the video is history about solving equations of 2, 3, 4 degree
And in number theory idea is talking about history about prime numbers, like they discovers❤
Love ya and your content❤!)

[bjornfeuerbacher]

I used the same steps until arriving at the inequality at 0:32, then I essentially solved it graphically: I imagined the hyperbola described by 1/x and figured out which parts of it lie above the line y = -7. That is _much_ faster than both the solutions shown in the video and in other comments here.

[mathmachine]

cbrt(1/x-1)>=-2

The cube root is monotonically increasing. Therefore,

1/x-1>=-8
1/x>=-7
x>0 or x<=-1/7

[sharonk]

Thank you for this solution, Professor @Luca

[tobyendy]

Great video like damn holy this is good

[Captaintrippz]

(-∞, -1/7]
Will edit when shown wrong in video.