Harvard University Interview Tricks
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- Опубліковано 7 лют 2025
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How to solve this Harvard University Problem
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Excelente explicación, largo pero muy interesante. Lo repasaré nuevamente. Gracias
Good job
Thank for sharing
Fantastic, step by step process!🎉 Thank you.
Muy interesante, felicidades!!!
在台灣，這個問題...高一的學生就會了！
Parabéns, excelente trabalho.
Obrigado 🙏❤️🙏
❤❤❤❤❤❤❤
Excellent
Thank you so much 😀
Thank you for a long way to get a very small answer in quite large numerals.
( It would be interesting to hear that (sqrt(5) -1)/2 is a special ratio.)
This is correct work at 05:00. It is also correct at 09:00. At 11.08 we are looking at a quadratic. We know already what X is. It is ( root 5 - 2) because you just told us that it was.
But you are still doing well .The answer will be (17 -72X)(17 - 72X) I am checking with a calculator. Still right at 18.00 so you did very well , but we are a generation that like short cuts.
他慢慢的把題目算成了我看不懂的樣子😂
😂
I simplified it to (1/Φ)^24 where phi is the golden ratio.
I’m a little lost at the following step regarding the denominator:
(Square root of 5)^2 - (square root of 1)^2. Should not the 1^2 part that is showing be (-1)^2? Thus making the result for the denominator 25 + 1 (26) instead of 25 - 1 (24)? I could see 24 if it were showing “ - (1)^2 “. But the 1 is showing no parenthesis between it and the negative sign.
Forgive this old, old man. Just want to enjoy things that I have forgotten.
The numerator is greater than the denominator; the result must be less than 1!
Yes it less than 1
@@passakornuprakam5198√5= 2.236, so the result will be 5.4
Much too long, but you do explain things. I solved it on my own and watched your steps.
simplify Sq.root 6
All numbers (under √) here, are multiples of √6.
Since denominator > numerator, let us call it 1/t = (√24)/(√30 + √6) = [√6.√4]/[√6.√5 + √6.√1] = √6[√4]/√6[√5 + √1] = 2√6/√6[√5 + 1],
Canceling out √6 in Denom. & Num. ⇒1/t = 2/(√5 + 1)
∴ t = (√5 + 1)/2.
Since 1/t = 2/(√5 + 1). Multiply both Num. & denom. with the conjugate of denominator,
1/t = 2(√5 -1)/(√5 + 1)(√5 -1) = 2(√5 -1)/((√5)² -1²) = 2(√5 -1)/((5) -1) = 2(√5 -1)/4 =(√5 -1)/2.
(1/t)+1 = (√5 -1)/2 + (2/2) = (√5 -1+2)/2 = (√5+1)/2 = t.
Also, (1/t) = t -1
Hence we established that
(1/t)+1 = t
t = (1/t)+1, multiplying with t throughout,
t²=1 +t.
t³ = t².t = (1 +t)t = t+t²=t+(t+1)=2t+1.
t⁴ = (1 +t)² = 1+2t+t². Substituting for t² =1+t, on LHS,
t⁴ =1+2t+(1+t) = 3t+2.
t⁸ = (t⁴)² =(3t+2)² = 9t²+6t+2² = 9(1+t)+6t+4 = 15t+13
(1/t)² = (t -1)²=t² -2t+1 =(t+1)-2t+1 = - t+2
(1/t)³ = (1/t)²(1/t) = (-t+2)(t -1) = -t² +3t -1 = -(1 +t+3t -1 =
(1/t)⁴ =((1/t)²)² = (-t+2)² = t² -4t+4 = (t+1) -4t+4 = -3t+5
(1/t)⁸ =((1/t)⁴)² = (-3t+5)² = 9t² -30t+25 =9(t+1) -30t+25 = -21t+34
Recalling the value of t, in the original equation,
(1/t)²⁴= ((1/t)⁸)³ = (-21t+34)³=(34 -21t)³= 34³+3(34²)(-21t)+3(34)(-21t)²+(-21t)³= - 9261t³+(102))(441)t²= - 9261t³+ 44982t² -72828t+34³
= - 9261(2t+1)+ 44982(t+1) --72828t+39304 = -46368t+75025 . . . putting the value for t,
= - 46368(√5 + 1)/2 +75025 = -23184√5 + 51841.
La respuesta da cero?
Tiende a cero, es muy pequeño.
The solution is very lengthy and it is not suggestible to the students
🎉 0:36
😅😢😂❤😂😊❤ 0:47
Tiene un error en los signos
Such a long process, not sure if it’s worth the time
I think the answer is one, maybe i am wrong?
+
16
I'm not very good at math at all, but shouldn't (√5-2)^8 be solved by binomial theorem?I know it's a big power, but maybe Pascal's triangle would work too... I'm a beginner in math, so I'm sorry if I'm wrong...(a+b)^8=a^8+8a^7b+28a^6b^2+56a^5b^3+70a^4b^4+56a^3b^5+28a^2b^6+8ab^7+b^8. might be super annoying with the larger coefficients...
root(5) -2 is a small thing, and the answer is very small indeed , when repeatedly multiplied by itself, but use a calulator too. At least the calculator will become a good friend.
Boş bir soru. Hiç geliştirici yanı yok.
🤣
算数，脑部运动防止老年痴呆
My math, your math❌ / Our math ✔️
Ответ не правильный
Ответ неправильный,ошибка есть
ጥፍ
Wrong.
You can calculate by calculator.
How so? The answer is correct.
@@bentels5340 I think he just makes a mess by keyboard like a kid.
Porqueira em português já é complicado agora vc. Imagina o cara explicando essa porqueira em grego.