Harvard University Admission Interview Tricks.✍️🖋️📘💙
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- เผยแพร่เมื่อ 31 ธ.ค. 2024
- University Admission Exam Question || Algebra Problem || Entrance Aptitude Simplification Test || Tricky Interview
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quicker and easier if you calculated y^6 first
then set m=y^6/729
on the way calculate y^2 and y^3 and check
3y^2 +y^3
= (12-6_/3) +(-10 +6_/3)
=2 as required.
y^6= (-10+6_/3)^2
=208-120_/3
m=y^6/729
=208/729 -40/243
❤❤
🥳🎉🎁✅
other way to solve the equation y³ + y² - 2/27 = 0
1. Find a solution by inspection. I found one after trying three fractions
2. the solution ist y = - 1/3
3. factorize y³ + y² - 2/27 = ( y + 1/3 )( y² + ay - 2/9 )
4. the factorizing can be found by long division --> a =+2/3
5. solving ( y + 1/3 )( y² + 2y/3 - 2/9 ) =0
6. solution 1: y = - 1/3 isn't a solution, while y must be positive
7 solution 2: y =- (-1-root(3))/3 isn't a solution, while y must be positive
8. solution 3: y -= (-1+root(3))/3 is a solution, while y is positive
9. for y ^6 calculate {(-1+root(3))/3]² * {(-1+root(3))/3]² * {(-1+root(3))/3]²
y can be negative!
m must be positive but a negative y can still give a positive m; m=y^6
Thanks for your nice question. A negative y is inconsistent to the domain of m. Therefore negative y MUST be disregarded.🥳🎉🎁🎄🌲
10^х+100^х=1000^х
10^х+10^2х=10^3х
10^х*(1+10^х)=10^3
Делим обе части равенства на 10^х, 10^x не равен 0 в любом случае
1+10^х=10^2х
10^2х-10^х-1=0
Замена10^х=а
а^2-а-1=0
Ищем корни
Д=(-1)^2-4*1*(-1)=1+4=5
а=(1+5^(1/2))/2
или а=(1-5^(1/2))/2
Ищем х
1 случай
10^х=(1+5^(1/2))/2
lg10^x=lg((1+5^(1/2))/2) lg10^x=x*lg10=x*1=x
x=lg(1+5^(1/2)/2)
lgb,b>o