Spain | A Nice Algebra Problem | Math Olympiad
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- Опубліковано 12 жов 2024
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imo
Find the value of x?
How to solve √1 + √1+x = ∛x
In this video, we'll show you How to Solve Math Olympiad Question A Nice Radical Equation √1 + √1+x = ∛x 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
x=0 and x=-1 are not solutions
x=8 is the only solution
You are right! ❤
Yes, verification needed.
True, but the math is correct. How to explain ?
@@ChrisManton It's called an extraneous solution. It is like a fake root resulted from a transformed equation which is not directly the same as the original equation. Take ✓x = -1 for example, squaring both sides gives us x = 1, but we know ✓1 is 1, not -1, so 1 is an extraneous solution. So there it is, that's the answer.
@@CheesedogIsWhat I always wished sqrt(x) was a direct inverse of x^2
Spoiler blocker 🛡️ 🛡️ 🛡️
Thank you for explaining. The solution is only x=8.
you are welcome! ❤
(1+x) =( x^(2/3) - 1)^2
1+x = x^(4/3) - 2x^(2/3) + 1
x = x * x ^(1*3) - 2x^(2/3)
1= x ^(1/3)- 2*x^(-1/3)
Let y = x^(1/3)
1 = y - 2 /y
y^2 - y - 2 =0
(y-2)(y+1)=0
Solution 1
y = 2; x^(1/3)= 2; x=8
Solution 2
y = -1 ; x^(1/3)=-1;
x= -1 帶入原式不合
非解 ！
Very nice trick! ❤
First solution: x = - 1
√[1 + √(1 + x)] = ³√x → where: x = - 1
√[1 + √(1 - 1)] ? ³√(- 1)
√[1 + 0] ? (- 1)^(1/3)
√1 ? - 1
1 ≠ - 1 → x = - 1 must be rejected
Second solution: x = 0
√[1 + √(1 + x)] = ³√x → where: x = 0
√[1 + √(1 - 0)] ? ³√(0)
√[1 + √(1)] ? 0
√[1 + 1] ? 0
√2 ≠ 0 → x = 0 must be rejected
Very nice! I really appreciate that ❤
Не верно
Если подставьте х=0
0=sqrt 2,
Если подставить х=-1
1=-1, что тоже не верно
Поэтому корень один х=8, о чём не сказано, значит корня получается три. Ответ полностью не верно
большое спасибо!
x = 8 включено в решения, но я забыл проверить значения x. Извините за неудобства! ❤
Din cele 3. Sol.doar x=8 verifica ec. Data
Da, ai dreptate 8 este singura solutie ❤