In this video, we solve the following system of equations:
1) √x + √3 = 10
2) √xy = 10
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Step-by-Step Solution:
1) Squaring the First Equation: We start by squaring both sides of the first equation to eliminate the square roots, leading us to a quadratic form.
2) Substituting Variables: Next, we manipulate and substitute the variables to simplify the equations further.
3) Formulating a Quadratic Equation: By substituting the simplified expressions, we derive a quadratic equation that allows us to solve for X_1,2 and Y_1,2.
4) Applying the Quadratic Formula: Using the quadratic formula, we calculate the possible values for X_1,2.
5) Determining yyy: Finally, we substitute the values of x back into the equations to find the corresponding values of Y_1,2.
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Key Concepts Covered:
1) Radical Equations:
Understanding and applying properties of radicals.
Simplifying and solving equations involving square roots.
2)Algebraic Manipulation:
Substitution method to solve systems of equations.
Using quadratic formula to find solutions.
3)Step-by-Step Problem Solving:
Detailed breakdown of each step to ensure clear understanding.
Combining and simplifying expressions efficiently to isolate variables.
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Learning Outcomes:
By the end of this video, you will:
- Understand how to manipulate and simplify equations involving radicals.
- Be able to apply algebraic methods to solve systems of equations.
- Gain confidence in breaking down and solving intricate math problems step-by-step.
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Also you can see:
• How to Solve Radicals ...
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Tags:
Exponential Equations, Algebra, Math Tutorials, Educational Math Videos, Fun Learning, SciMarvels Channel, Math Without Voiceover, Visual Learning, Exponent Rules, Algebraic Simplification, KZread Math, Math Education, Algebra Techniques, Interactive Math, Science and Math Fun, Algebraic Solutions, Silent Math Tutorial, Educational Content, Step-by-Step Solution, Non-Linear Equations.