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 Radical E...
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