A HARD Entrance Exam Question | 84% FAILED to answer correctly

High School Entrance Examination | A tricky challenge
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[@jiudoka8791]

Thanks! A wonderful logical discription about this Mathe-Task. 🙂

[@WheelForce]

It's not that hard. Once you find a linear expression for the number in the brackets squared, the path to the answer is clear. Just multiply that squared expression by itself again and again (and also once by the original number, if need be) until you reach the wanted exponent of the original number.

[@RealQinnMalloryu4]

(3 ➖ 1/2)2^5 (3 ➖ 1/1)2^1 (3 ➖/)^2 (x ➖ 3x+2).

[@ItsPREPP98]

We could also use Pascal's triangle 1. 1. 1. 2. 1. 1. 3. 3. 1 1. 4. 6. 4. 1 1. 5. 10. 10. 5. 1 1. 6. 15. 20. 15. 6. 1 1. 7. 21. 35. 35. 21. 7. 1 1. 8. 28. 56. 70. 56. 28. 8. 1 1. 9. 36. 84. 126. 126. 84. 36. 9. 1 1. 10. 45. 120. 210. 252. 210. 120. 45. 10. 1 Hence, (√3-1)^10 = (√3)^10 - 10(√3)^9 + 45(√3)^8 - 120(√3)^7 + 210(√3)^6 - 252(√3)^5 + 210(√3)^4 - 120(√3)^3 + 45(√3)^2 - 10(√3) + 1

[@Gunner98]

If you know how binomial expansion works you don't need to write down the Pascal's triangle everytime

[@ItsPREPP98]

@@Gunner98 yea well don't really know it. wait I'll search it up...

[@charlesbrowne9590]

You haven’t finished. The difficulties you have yet to encounter should help you appreciate the technique used here.

[@ItsPREPP98]

@@charlesbrowne9590honestly, doing that on pen and paper is easy af. The difficulties arise only in keyboard

[@albertomontori2863]

in italy is known as Tartaglia's triangle

[@maikellaishram7484]

What about using binomial expansion

[@janami-dharmam]

you will get the same result