A very tricky Harvard University Admission Algebra Exam | Entrance Aptitude Test | Find x!!

[@shubhayubanerjeedpsn-std5526]

answer is -2, solved it in within 10 seconds of seeing question other solution takes time

[@AsadInternationalAcademy]

Great!!

[@AsadInternationalAcademy]

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[@AsadInternationalAcademy]

please show your steps to get -2 in 10 seconds!

[@raxadorous607]

@@AsadInternationalAcademy well we know the number must be negative since if it were positive, x^2 would be < x^3; if that were true we would get a negative number. we know its negative because a negative number squared is positive, and a negative picture cubed is negative. we know a positive minus a negative is the same as adding. so what numbers could we get to add up to 12? its easy to figure out that 8 and 4 work, because (-2)^2 is 4, and (-2)^3 is 8. 4+8=12

[@uhlamp4733]

@@raxadorous607wish that (-2)^3 was 8… it’s -8

[@OnestateCoding]

Factorized LHS only once, took log on both sides, simplified. Got x = ±2. Checked. Answer is -2. Solved within like 10 sec just by looking at the question.

[@OnestateCoding]

x²-x³ = 12 x²(1-x) = 12 log [x²(1-x)] = log 12 2log x + log (1-x) = 2log 2 + log 3 Simplified and got x = ±2. Checked in the first equation and got -1 as the valid answer.

[@AsadInternationalAcademy]

Awesome! thanks for this

[@AsadInternationalAcademy]

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[@AsadInternationalAcademy]

Perfect!

[@Zoro4Swords]

Bruh I did it orally. The answer is -2. This is class 9 algebra in india, why is Harvard asking this 😭

[@Zoro4Swords]

How I did it orally? Well, the value of the x^3 is more than x^2 obviously So, x must be negative number so that the final value could be positive (since it's -x^3) Thus, by an easy observation after this anyone can say -2 is the answer.

[@ijedjoshua]

it's clickbait

[@AsadInternationalAcademy]

Good job, this is practice for the exam of Harvard entrance

[@AsadInternationalAcademy]

no

[@AsadInternationalAcademy]

Nice

[@victorsingh8456]

Pretty easy if we go by observation x^2(1-x) = 12 we know that: 12 = 2 x 2 x 3 by observation we can see that we need to put a value of -2 in the above equation to get 3 inside the bracket of LHS thus (-2)^2(1-(-2)) (4)x(3) = 12 thus x = -2

[@Lucas-g9i6y]

and im guessing its also pretty easy to get x=(3+sqrt(15)*i)/2

[@AsadInternationalAcademy]

Amazing!

[@AsadInternationalAcademy]

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[@AsadInternationalAcademy]

Good

[@AsadInternationalAcademy]

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[@irshadtufail7097]

Nicely explained

[@AsadInternationalAcademy]

Thank you so much 🙂

[@ali-faizyab]

I just guessed it orally ( -2 )... btw it seemed easy ;D

[@AsadInternationalAcademy]

Really? Good job.

[@AsadInternationalAcademy]

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[@sen-ni8ri]

I am new to this, how are you able to divide 0 by negative?

[@AsadInternationalAcademy]

I mean, divide by (-1) on both sides

[@AsadInternationalAcademy]

0 divided by any number positive or negative always equals to zero in maths, (100% true, ask your class teacher)

[@AsadInternationalAcademy]

I hope you understood! Watch 110+ most important olympiad questions with solutions by just clicking on the link below kzbin.info/aero/PLybCHBiqtqWP-TrcsG21MXXxlknROi514 Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!

[@sen-ni8ri]

@@AsadInternationalAcademy okay ah yes, sorry I got the numbers mixed up, knowing if it were -1/0 it would be undefined. Thank you sorry for the misunderstanding

very nice explanation mr.Asad! :)

[@AsadInternationalAcademy]

Thanks for liking

[@AsadInternationalAcademy]

Watch 110+ most important olympiad questions with solutions by just clicking on the link below kzbin.info/aero/PLybCHBiqtqWP-TrcsG21MXXxlknROi514 Don't forget to share this link with your classmates so that they also have a benefit of it. Please, like and subscribe this channel including pressing bell icon to get the notification of new video!