Explaining And Solving The Equation Sqrt(1+3X*X^3)

Integral of sqrt(x)/sqrt(1x^3) (substitution) YouTube from www.youtube.com

Understanding the Equation

The given equation is sqrt(1+3x*x^3). To solve this equation, we need to understand the basic mathematical operations involved in it. The square root symbol (√) indicates that we need to find the number that, when multiplied by itself, gives the value inside the bracket. In this case, the value inside the bracket is 1+3x*x^3.

Simplifying the Equation

To simplify the equation, we need to simplify the expression inside the bracket. We can do this by multiplying x with x^3, which gives x^4. So, the expression inside the bracket becomes 1+3x^4.

Applying the Square Root

Now that we have simplified the expression inside the bracket, we can apply the square root to the entire expression. So, the equation becomes sqrt(1+3x^4).

Solving the Equation

To solve the equation, we need to find the value of x that makes the expression inside the square root equal to zero. We can do this by setting 1+3x^4 equal to zero and solving for x.

Setting the Expression to Zero

1+3x^4=0

Solving for x

Subtracting 1 from both sides, we get: 3x^4=-1 Dividing both sides by 3, we get: x^4=-1/3 Taking the fourth root of both sides, we get: x=(-1/3)^(1/4)

Final Answer

Therefore, the solution to the equation sqrt(1+3x*x^3) is x=(-1/3)^(1/4).

Real-World Applications

The square root function is commonly used in many real-world applications, such as calculating the length of the sides of a right triangle or calculating the distance between two points in a coordinate plane. It is also used in engineering and physics to calculate the magnitude of quantities such as force or energy.

Conclusion

In conclusion, the given equation sqrt(1+3x*x^3) can be simplified to sqrt(1+3x^4) and solved by setting 1+3x^4 equal to zero and solving for x. The final solution is x=(-1/3)^(1/4). The square root function is a fundamental mathematical operation that has many real-world applications in various fields.