A nice exponential equation.

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[vladimirrodriguez]

In the first option the solution should be x=(-5+-sqrt(17))/2 and in the second option the solution should be x=(10+-sqrt(152))/2. It was considered all possible solutions to the problem, nice resolution 👍

[darkmask]

1st case x should be (-5±sqrt(17))/2
2nd case x should be 5±sqrt(38)

[finnabraun]

i’m about to take my first college math class as a junior in high school, and your videos keep me excited for what lies ahead

[skit_inventor]

I heard that a similar problem (if not actually this one) caused a great deal of dispute because the last solution falls out of the usual "non-negative base" restriction of the exponential function. Especially when the problem states "find all _real_ solutions", which kinda implies that the function be treated like an exponential function, and all cases where the base is negative and the exponent happens to be an integer should be discarded. Or, similarly, you can rewrite the original function in terms of the log, which automatically sets the mentioned restriction.

Tl;dr unless you specify whether you allow the function to be defined at a discrete (in this case) set of points with a negative base and an integer exponent, the actual set of solutions might vary depending on the solver's interpretation of the problem

[nadavslotky]

Actually, it's easy to see that the exponent is for every integer x, as it is either the sum of 3 even numbers or two odds and an even, but that's probably an overkill

[emulateiam]

what if the RHS is equal to something other than 1?

oh I guess it would just divide out

[mFix]

is function x^x defined for non positive x? I doubt it

[cd-zwtt]

So zero exponents don't always end up at 1! How can you use this same reasoning to show that 0^0 is indeterminate, I wonder?

[deep]

If the difference of the gcd and the lcm of two numbers a and b is 57 then what is the minimum value of a+b ?

[Grizzly]

Sorry, got to give a downvote for ballsing up the solutions to those first two quadratics.