A Nice Algebra Problem | Math Olympiad | Solve for x and y?
ฝัง
- เผยแพร่เมื่อ 9 ก.พ. 2025
- math olympiad
olympiad math
math olympiad question
math olympiad questions
math olympiad problem
math olympiad problems
olympiad math problems
algebra olympiad problems
math
maths
algebra
algebra problem
nice algebra problem
a nice algebra problem
equation
exponential equation
a nice exponential equation
radical equation
a nice radical equation
math tricks
imo
Find the value of x and y?
How to solve √3^√x - √2^√y = 17
In this video, we'll show you How to Solve Math Olympiad Question A Nice Algebra Problem √3^√x - √2^√y = 17 in a clear , fast and easy way. Whether you are a student learning basics or a professtional looking to improve your skills, this video is for you. By the end of this video, you'll have a solid understanding of how to solve math olympiad exponential equations and be able to apply these skills to a variety of problems.
#matholympiad #maths #math #algebra
Υπέροχα,μεθοδικά,κατανοητά,μαγικά... ευχαριστώ πολυ🎉❤
Είστε πολύ ευπρόσδεκτοι!
Eíste polý efprósdektoi! ❤
@SALogics Ευχαριστώ πολύ κι εσείς συνεχίστε έτσι όμορφα να μας διδάσκετε🤗Thank you very much and please continue to teach us so beautifully🤗
Kinda easy equation.
Very nice! ❤
@@SALogics Russian students solve much harder equations :)
let √3^√x=a , √2^√y=b so a-b=17
(a^1/2+b^1/2)(a^1/2-b^1/2)=17•1
a^1/2+b^1/2=17 and a^1/2-b^1/2=1
2a^1/2=17+1=18 , a^1/2=9,a=81
a^1/2+b^1/2=17 and a^1/2=9
9+b^1/2=17 , b^1/2=8 , b=64
a=81 , √3^√x=81=3^4=√3^8
√3^√x=√3^8 ,√x=8 , x=64
√2^√y=b =64=2^6=√2^12
√y=12 , y=144
Very nice! ❤
x=64, y=144 :)
Very nice! ❤
let u=(V3)^((Vx)/2) , let v=(V2)^((Vy)/2) , u^2-v^2=17*1 , let u+v=17 , let u-v=1, u+v+(u-v)=17+1 , 2u=18 , u=9 ,
u^2=81 , (V3)^(Vx)=81 , Vx=log81/log(V3) , Vx=8 , x=64 , 81-17=64 , (V2)^(Vy)=64 , Vy=log64/log(V2) , Vy=12 , y=144 ,
test , (V3)^(V64)-(V2)^(V144)=81-64 , --> 17 , OK , solu , x= 81 , y=144 ,
Very nice! ❤
@@SALogics Thanks!