Germany l| Can you solve this?? l Olympiad Math exponential problem✍️🖊️💯

[@shubhamdwivedi1432]

Best way to make the solution difficult.

[@E.h.a.b]

let 2^a = x then we get
a = Ln(x)/Ln(2) //Condition : x > 0
x + 1/x = 4
x^2 - 4 x + 1 = 0 //Multiply by x
x = (4 +/- √(16-4(1)(1)) )/2
x = (4 +/- 2√3 )/2 = 2 +/- √3
x = 2 +/- √3 //We will accept both roots since they both are greater than zero
a = Ln(2 +/- √3) /Ln(2)

[@eamonhannon1103]

You explained the rules very well apart from one rule you did not explain . This was at -8:36 .

[@Mamtamaam]

Thanks 🙏

[@ChavoMysterio]

2^a+2^-a=4
2^a+[1/(2^a)]=4
Domain: a>0
Let b=2^a
b+(1/b)=4
b²+1=4b
b²-4b+1=0
b²-4b+4=3
(b-2)²=3
|b-2|=√3
b-2=±√3
b=2±√3
2^a=2±√3
a=log_2(2±√3) ❤❤

[@KHWLADjmen]

Tam

[@Nimékwa]

2-a*4=8
8=2³=2a
4=2²=2-a
2³-2²=4

[@aruntiwari5714]

Nice solution

[@MrPoornakumar]

Let 2^a = x.
Then
x+x^-1=4
Multiplying with x & re-arranging the terms,
x^2 -4x +1=0
This is a quadratic equation {with a = 1, b= -4, c=1},
Roots are = ½[4±√(16 -4)] = ½[4±√(12)] = ½[4±√(12)] = ½[4±√(3 . 4)] = ½[4±2√(3)]= 2±√3
Since x = 2^a,
2^a = 2±√3.
Take log on both sides
log(2^a) = log(2±√3)
a log2 = log(2±√3). Divide by log(2) on both sides
a log2/log2 = log(2±√3)/log2
Cancelling out log2 terms in numerator & denominator on LHS
a = log(2±√3)/log2
I call "log2()" as log to the base 2 of () & log2(2) = 1.
a = log2(2±√3)/log2(2) = log2(2±√3)/1 = log2(2±√3) = log2(2+√3), log2(2 -√3)
The numerical values need to be found.
a = log2(2+1.7321), log2(2 -1.7321) = 1.1547, 0.267849

[@satyadev3848]

good teacher

[@arvindkulkarni6580]

Well it's very difficult steps

[@KeshavKulkarni-x1w]

All steps are correct

[@BUDDHIST_RASHTRA]

Yes

[@LaxmanKumar-yi4cv]

Achha video hey maam

[@DarshChouhan-r6g]

tricky solution thanks

[@walterwen2975]

Germany, Olympiad Math exponential problem: 2ª + 2⁻ª = 4; a =?
4 > 2ª > 2⁻ª > 0 or 4 > 2⁻ª > 2ª > 0; 2ª + 2⁻ª = 2ª + 1/2ª = 4, (2ª)² - 4(2ª) + 1 = 0
(2ª - 2)² = 3 = (√3)², 2ª = 2 ± √3 > 0, a = log₂(2 + √3) or a = log₂(2 - √3)
Answer check:
a = log₂(2 + √3): 2ª = 2^log₂(2 + √3) = 2 + √3, 2⁻ª = 1/(2 + √3) = 2 - √3
2ª + 2⁻ª = (2 + √3) + (2 - √3) = 4; Confirmed
a = log₂(2 - √3): 2ª = 2^log₂(2 - √3) = 2 - √3, 2⁻ª = 1/(2 - √3) = 2 + √3
2ª + 2⁻ª = (2 - √3) + (2 + √3) = 4; Confirmed
Final answer:
a = log₂(2 + √3) = 1.9 or a = log₂(2 - √3) = - 1.9
The calculation was achieved on a smartphone with a standard calculator app

[@NithyaGhumare]

❤❤

[@pedroborges4986]

Lindo demais da conta!!!!!

[@harikishan1900]

Very well done

[@SOBIESKI_freedom]

Not "both side"; it's "both sides" (plural).

[@deep.00]

U should not use a=1
Better change question
Use variable x instead of a in question.

[@KhushiTtripathi]

Nice method maam

[@mariame6261]

It's not that hard

[@mrdong5796]

Vous parlez trop.