1 Divided By 2^1/3 +2 -1/3=C/d(2 2/3 +2^-2/3 -1) Then The Value Of D/c=

Mar 8, 2025 by ADMIN 73 views

Solving the Equation: 1 divided by 2^1/3 + 2^-1/3 = C/d(2^2/3 + 2^-2/3 - 1)

In this article, we will delve into the world of mathematics and solve a complex equation involving exponents and fractions. The equation given is 1 divided by 2^1/3 + 2^-1/3 = C/d(2^2/3 + 2^-2/3 - 1). Our goal is to find the value of d/c.

Understanding the Equation

To begin, let's break down the equation and understand its components. We have two main parts:

2^1/3 + 2^-1/3
2^2/3 + 2^-2/3 - 1

The first part involves adding two fractions with different denominators, while the second part involves adding two fractions with different denominators and then subtracting 1.

Simplifying the First Part

Let's start by simplifying the first part of the equation: 2^1/3 + 2^-1/3.

We can rewrite 2^1/3 as √[2^2] and 2^-1/3 as 1/√[2^2]. This gives us:

√[2^2] + 1/√[2^2]

Now, we can combine the two fractions by finding a common denominator, which is √[2^2]. This gives us:

(√[2^2] + 1)/√[2^2]

Simplifying further, we get:

(2 + 1)/√[2^2]

Which equals:

3/√[2^2]

Simplifying the Second Part

Now, let's simplify the second part of the equation: 2^2/3 + 2^-2/3 - 1.

We can rewrite 2^2/3 as (√[2^2])2/3 and 2^-2/3 as 1/(√[2^2])2/3. This gives us:

(√[2^2])2/3 + 1/(√[2^2])2/3 - 1

Now, we can combine the two fractions by finding a common denominator, which is (√[2^2])2/3. This gives us:

(√[2^2])2/3 + 1/(√[2^2])2/3 - (√[2^2])2/3

Simplifying further, we get:

1/(√[2^2])2/3 - (√[2^2])2/3

Which equals:

1/2 - 2/3

Substituting the Simplified Parts

Now that we have simplified both parts of the equation, we can substitute them back into the original equation:

1 / (3/√[2^2]) = C/d(1/2 - 2/3 - 1)

Simplifying the left-hand side, we get:

√[2^2] / 3 = C/d(1/2 - 2/3 - 1)

Finding the Value of d/c

To find the value of d/c, we need to simplify the right-hand side of the equation:

C/d(1/2 - 2/3 - 1)

First, let's simplify the expression inside the parentheses:

1/2 - 2/3 - 1

We can rewrite 1/2 as 3/6 and 2/3 as 4/6. This gives us:

3/6 - 4/6 - 1

Which equals:

-1/6 - 1

Now, we can combine the two fractions by finding a common denominator, which is 6. This gives us:

-1/6 - 6/6

Which equals:

-7/6

Now, we can substitute this value back into the original equation:

√[2^2] / 3 = C/d(-7/6)

Simplifying the left-hand side, we get:

2/3 = C/d(-7/6)

Now, we can cross-multiply to get:

2d = -7C/3

Dividing both sides by 2, we get:

d = -7C/6

Now, we can divide both sides by C to get:

d/c = -7/6

Therefore, the value of d/c is -7/6.

In this article, we solved a complex equation involving exponents and fractions. We simplified the equation by breaking it down into smaller parts and then combining them. We found that the value of d/c is -7/6. This equation is a great example of how mathematics can be used to solve real-world problems.
Frequently Asked Questions: 1 divided by 2^1/3 + 2^-1/3 = C/d(2^2/3 + 2^-2/3 - 1)

Q: What is the main concept behind this equation?

A: The main concept behind this equation is the use of exponents and fractions to simplify complex expressions. The equation involves adding and subtracting fractions with different denominators, and then using algebraic manipulations to solve for the value of d/c.

Q: What is the significance of the equation 2^1/3 + 2^-1/3?

A: The equation 2^1/3 + 2^-1/3 is significant because it involves adding two fractions with different denominators. By simplifying this expression, we can find a common denominator and combine the two fractions.

Q: How do you simplify the expression 2^2/3 + 2^-2/3 - 1?

A: To simplify the expression 2^2/3 + 2^-2/3 - 1, we can rewrite 2^2/3 as (√[2^2])2/3 and 2^-2/3 as 1/(√[2^2])2/3. This allows us to combine the two fractions by finding a common denominator.

Q: What is the value of d/c?

A: The value of d/c is -7/6. This was found by simplifying the equation and using algebraic manipulations to solve for the value of d/c.

Q: How does this equation relate to real-world problems?

A: This equation is a great example of how mathematics can be used to solve real-world problems. By simplifying complex expressions and using algebraic manipulations, we can find solutions to problems that may seem impossible at first.

Q: What are some common applications of this type of equation?

A: This type of equation has many common applications in fields such as physics, engineering, and computer science. For example, it can be used to model population growth, electrical circuits, and computer algorithms.

Q: How can I apply this equation to my own work or studies?

A: To apply this equation to your own work or studies, you can use it to model complex systems and find solutions to problems that may seem impossible at first. You can also use it to simplify complex expressions and find common denominators.

Q: What are some common mistakes to avoid when working with this type of equation?

A: Some common mistakes to avoid when working with this type of equation include:

Not finding a common denominator when adding or subtracting fractions
Not simplifying complex expressions before solving for the value of d/c
Not using algebraic manipulations to solve for the value of d/c

Q: How can I practice and improve my skills with this type of equation?

A: To practice and improve your skills with this type of equation, you can try working on similar problems and exercises. You can also use online resources and study guides to help you learn and understand the material.

In this article, we answered some of the most frequently asked questions about the equation 1 divided by 2^1/3 + 2^-1/3 = C/d(2^2/3 + 2^-2/3 - 1). We covered topics such as the main concept behind the equation, the significance of the equation 2^1/3 + 2^-1/3, and the value of d/c. We also discussed common applications of this type of equation and provided tips for practicing and improving your skills.