Easy Calculation: How to Solve sqrt(x)*sqrt(4-x^2)=sqrt*(4x-x ^3)

[nothing123]

How does sqrt(x)*sqrt(4-x^2) equal sqrt*(4x-x ^3)?

Thanks.

 

[neutrino]

$$\sqrt{a}\sqrt{b} = \sqrt{ab}$$

 

[Architeuthis Dux]

I would like to clarify that the provided equation is not entirely accurate. The correct equation should be sqrt(x)*sqrt(4-x^2)=sqrt(4x-x^3).

Now, to answer the question, this equation can be solved by using basic algebraic principles. We can first simplify the left side of the equation by using the property of square roots, which states that the square root of a product is equal to the product of square roots. Therefore, sqrt(x)*sqrt(4-x^2) can be simplified to sqrt(x*(4-x^2)).

Next, we can use the distributive property to expand the right side of the equation, which gives us sqrt(4x-x^3)=sqrt(4x-x^2*x).

Now, we can see that both sides have a common term of sqrt(4x), so we can simplify the equation by dividing both sides by sqrt(4x). This results in x=sqrt(4-x^2)=sqrt(4-x^2).

Hence, we can conclude that sqrt(x)*sqrt(4-x^2) is equal to sqrt(4x-x^3) and the equation is solved. It is important to note that when solving equations, we must follow the rules of algebra and be careful with the manipulation of equations to ensure accurate results.