✅Video Overview:
Welcome to SciMarvels, where complex math problems are simplified and solved with ease. In this video, we delve into solving the equation x√x = x + √x. Watch as we break down the problem step-by-step, using algebraic manipulation and quadratic formulas to find the values of x. Join us and enhance your understanding of mathematical problem-solving techniques.
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✅ Key Concepts Covered:
• Algebraic manipulation
• Substitution method
• Solving cubic equations
• Applying the quadratic formula
Detailed Steps
1. Given: x√x = x + √x
(√x)^2√x = (√x)^2 + √x
Let √x = t
2. Transforming the equation
t^2 t = t^2 + t then: t^3 = t^2 + t
3. Forming a cubic equation
t^3 - t^2 - t = 0 So: t(t^2 - t - 1) = 0
4. Solving the equation
- (I) t = 0
√x = 0 then x = 0
- (II) t^2 - t - 1 = 0
a = 1, b = -1, c = -1
- Applying the quadratic formula t_(1,2) = (-b ± √(b^2 - 4ac)) / 2a
t_{1,2} = (1 ± √5) / 2
5. Recalling √x = t
- (I) √x = 0 then: x = 0 ✅
- (II) √x = (1 + √5) / 2 then: x = [(1 + √5) / 2]^2 ✅
- (III) √x = (1 - √5) / 2 is negetive! So it can not be the answer! ❌
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✅ Learning Outcomes:
By the end of this video, you will:
• Understand how to manipulate algebraic expressions.
• Be able to solve cubic equations using substitution.
• Apply the quadratic formula to find real solutions.
• Gain confidence in solving complex mathematical problems step-by-step.
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• How to Solve Radical E...
• How to Solve Complex E...
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At SciMarvels, we simplify complex scientific concepts and make learning an enjoyable experience. Subscribe to our channel to access:
• Clear and concise problem-solving videos.
• A wide range of topics in physics and mathematics.
• Interactive and engaging learning methods.
• Regular content updates to keep you ahead in your studies.
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✅Tags:
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