High School Entrance Exam | Only 9% of students got this math question correct

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[Sqrt.Infinity]

As a person with eyes I solved it and got x = 2 within 10 seconds

[madelineveggie]

x=2 by inspection is one solution. period. This is ridiculous

[jeanlemire]

The obvious answer is x = 2. As can be seen, 2^2 = 4 and 4 + 2 = 6. If I rewrite the equation as 2^x + x - 6 = 0, I can plot the equation y = 2^x + x -6 and I quickly see that there is one real root at x = 2 and there is no complex root.

[BartBuzz]

I find it hard to believe that high school students are introduced to the Lambert W function.

[arthurmatthewf]

High schools don't have entrance exams. However, 8th graders do learn exponents. So, if a typical 8th grader can't immediately recognize the answer is '2', perhaps the issue is a fundamental flaw in education. And, where does the 9% come from??? Teaching this insanely complex solution to an 8th grader rather than just teaching to employ simple inductive/deductive reasoning will put the child 'off' of math forever. I taught University math and would never abuse college students this way.

[fubaralakbar]

You don't need W for this--however it is good that you explain it, because if you had a problem like 2^x+x=5, now you need W.
Fortunately, the problem here can be factored.
Factor out x for x(2^(x-1)+1=6
Now factor 6 into 2 and 3, guess and check. You find that for 2^(x-1)+1, a value of 2 yields 3--the other factor of 6. So x=2.

[Segalmed]

OK one trivial solution is x=2.
I'd have to check, whether there are further complex solutions.

[안진섭-bw]

램버트함수 안쓰는문제 제시해줌안되나
며칠에 한번 머리 쓴다생각하고 구독했는데 램버트함수문제 나오면 진이 쏙빠짐
이사람 인도사람임? 그렇지않고서는 자꾸 지수+미지수 문제 내는게 말이안됨
저번에도 램버트문제내서 댓글창 씹창났잖아

[X]

Very clever and I enjoyed the practice (even though by inspection x=2 would work nicely on a timed test). That said the Lambert W-Function is very handy and should be in every math major's "tool box".

[Roarshark]

I liked the second W() trick on the right side of the equation

[elloco]

This is idiotic and certainly not material for a high school entrance exam.

[vicebubble]

The function is increasing therefore it has almost once solution. If we replace X with 2 and it verifies the equation, we can stop.

[davidcarter]

Absurd solution. The obvious answer is 2, easily found in certainly not more than the 10 seconds it took sqrt. You have got to be public sector. No one in the private sector would waste 13 minutes doing something that should take 10 seconds.

[NothingMaster]

Half way through the exercise, your English accent took a beeline for your native language and became almost incomprehensible.

[GeorgeAlexanderOz]

Yeah, great, let's multiply by 2 to the power of 6, but don't ask why.

[dieterkohler]

Will you ever stop presenting problems that end in the W function?
Do you think that future high school students EVEN KNOW the W function? (Hint: the answer is NO)

[black_eagle]

This might be the silliest math channel on youtube. The solution is 2 by inspection, no need for the lambert W function, which pre-high school students don't know anyway. Ridiculous.

[kosterix]

Isn’t it obvious that 2 fits the bill?

[RealQinnMalloryu]

{2x+2x ➖ }+{x+x➖ }={4x^2+x^2 }=4x^4 (x ➖ 4x+4)

[prollysine]

we get, , 2^6=2^2+2^4, 2^2*ln2*e^(ln2)^4, 4*ln2*e^(4*ln2),
, -->, 4*ln2=(6-x)ln2, 4=6-x, x=6-4, x=2,
with W( 2^6*ln2) = 2.772588722, (6-x)*ln2=2.772588722, -->, x=6-2.772588722/ln2, -->, x=2, OK,