If √3/2/2+√3=a+b√c Find The Value Of A,b And C

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Introduction

In this article, we will delve into the world of algebra and mathematics to solve the given equation: √3/2/2+√3=a+b√c. This equation involves square roots and fractions, making it a challenging problem to solve. We will break down the equation step by step, simplify it, and finally find the values of a, b, and c.

Understanding the Equation

The given equation is √3/2/2+√3=a+b√c. To start solving this equation, we need to simplify the left-hand side by combining the fractions and the square roots.

Simplifying the Left-Hand Side

To simplify the left-hand side, we can start by combining the fractions:

√3/2/2+√3 = (√3/2)/2 + √3

We can simplify this further by multiplying the numerator and denominator of the fraction by 2:

(√3/2)/2 + √3 = (√3/2 × 2)/2 + √3 = (√3)/2 + √3

Now, we can combine the two square roots:

(√3)/2 + √3 = (√3 + √3)/2 = 2√3/2 = √3

So, the simplified left-hand side of the equation is √3.

Setting Up the Equation

Now that we have simplified the left-hand side, we can set up the equation:

√3 = a + b√c

Solving for a, b, and c

To solve for a, b, and c, we need to isolate the terms involving the square root. We can start by subtracting a from both sides of the equation:

√3 - a = b√c

Rationalizing the Denominator

To rationalize the denominator, we need to multiply both sides of the equation by the conjugate of the denominator. In this case, the conjugate of √c is √c. However, we don't know the value of c yet, so we will leave it as is.

Isolating b

We can isolate b by dividing both sides of the equation by √c:

(√3 - a)/√c = b

Isolating a

We can isolate a by multiplying both sides of the equation by √c:

a = √3 - b√c

Substituting the Value of a

We can substitute the value of a into the original equation:

√3 = (√3 - b√c) + b√c

Simplifying the Equation

We can simplify the equation by combining like terms:

√3 = √3

This equation is true for all values of b and c. However, we need to find specific values for a, b, and c.

Finding the Value of c

We can find the value of c by looking at the original equation. We know that the left-hand side involves the square root of 3, and the right-hand side involves the square root of c. Therefore, we can conclude that c = 3.

Finding the Value of b

Now that we know the value of c, we can find the value of b. We can substitute the value of c into the equation:

a = √3 - b√3

We can simplify this equation by combining like terms:

a = √3(1 - b)

Finding the Value of a

We can find the value of a by looking at the original equation. We know that the left-hand side involves the square root of 3, and the right-hand side involves the square root of c. Therefore, we can conclude that a = √3.

Substituting the Value of a

We can substitute the value of a into the equation:

√3 = √3(1 - b)

Simplifying the Equation

We can simplify the equation by dividing both sides by √3:

1 = 1 - b

Solving for b

We can solve for b by subtracting 1 from both sides of the equation:

b = 0

Conclusion

In this article, we solved the equation √3/2/2+√3=a+b√c and found the values of a, b, and c. We simplified the left-hand side of the equation, set up the equation, and solved for a, b, and c. We found that a = √3, b = 0, and c = 3.

Final Answer

The final answer is:

a = √3 b = 0 c = 3

Introduction

In our previous article, we solved the equation √3/2/2+√3=a+b√c and found the values of a, b, and c. However, we received many questions from readers who wanted to know more about the solution and the steps involved in solving the equation. In this article, we will answer some of the most frequently asked questions about the solution.

Q: What is the significance of the equation √3/2/2+√3=a+b√c?

A: The equation √3/2/2+√3=a+b√c is a mathematical equation that involves square roots and fractions. It is a challenging problem to solve, but it can be used to teach students about algebra and mathematical reasoning.

Q: How did you simplify the left-hand side of the equation?

A: We simplified the left-hand side of the equation by combining the fractions and the square roots. We started by combining the fractions:

√3/2/2+√3 = (√3/2)/2 + √3

We then simplified this further by multiplying the numerator and denominator of the fraction by 2:

(√3/2)/2 + √3 = (√3/2 × 2)/2 + √3 = (√3)/2 + √3

Finally, we combined the two square roots:

(√3)/2 + √3 = (√3 + √3)/2 = 2√3/2 = √3

Q: How did you find the value of c?

A: We found the value of c by looking at the original equation. We know that the left-hand side involves the square root of 3, and the right-hand side involves the square root of c. Therefore, we can conclude that c = 3.

Q: How did you find the value of b?

A: We found the value of b by substituting the value of c into the equation:

a = √3 - b√3

We then simplified this equation by combining like terms:

a = √3(1 - b)

We can then substitute the value of a into the equation:

√3 = √3(1 - b)

We can simplify this equation by dividing both sides by √3:

1 = 1 - b

We can then solve for b by subtracting 1 from both sides of the equation:

b = 0

Q: What is the significance of the value of b being 0?

A: The value of b being 0 means that the term b√c is equal to 0. This is because any number multiplied by 0 is equal to 0.

Q: Can you provide more examples of equations that involve square roots and fractions?

A: Yes, here are a few examples of equations that involve square roots and fractions:

  • √2/3 + √2 = a + b√c
  • √5/2 - √5 = a + b√c
  • √7/4 + √7 = a + b√c

These equations can be solved using the same steps as the original equation.

Q: How can I apply the solution to real-world problems?

A: The solution to the equation √3/2/2+√3=a+b√c can be applied to real-world problems that involve mathematical modeling and problem-solving. For example, you can use the solution to model the growth of a population or the spread of a disease.

Q: What are some common mistakes to avoid when solving equations that involve square roots and fractions?

A: Some common mistakes to avoid when solving equations that involve square roots and fractions include:

  • Not simplifying the left-hand side of the equation
  • Not isolating the terms involving the square root
  • Not rationalizing the denominator
  • Not checking the solution for extraneous solutions

By avoiding these common mistakes, you can ensure that your solution is accurate and complete.

Conclusion

In this article, we answered some of the most frequently asked questions about the solution to the equation √3/2/2+√3=a+b√c. We provided step-by-step explanations and examples to help readers understand the solution and the steps involved in solving the equation. We also provided tips and advice on how to apply the solution to real-world problems and how to avoid common mistakes when solving equations that involve square roots and fractions.