Can x=r solve the equations 1/squareroot(x+1)=x and x^3+x^2=1?

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In summary, the conversation discusses the process of solving the equation 1/squareroot(x+1)=x and finding the root r using algebra and simple iteration. The speaker is unsure how to show that x=r can solve the equation, but it is noted that this is essentially the same as saying that r is the root of the equation.
  • #1
gomes.
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[itex]y=1/squareroot(x+1)[/itex]
[itex]y=x[/itex]

Sketch the two graphs, and indicate on your graph the location of the root r of the equation [itex]1/squareroot(x+1)=x[/itex]. Use algebra and show that x=r can also solve the equation [itex]x^3+x^2=1[/itex]. Calculate r to 5 significant figurees using simple iteration.


Im stuck in the part in bold. I can rearrange [itex]1/squareroot(x+1)=x[/itex] into [itex]x^3+x^2=1[/itex], but how do i show that x=r can solve the equation? Thanks.
 
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hi gomes! :smile:

(have a square-root: √ and try using the X2 icon just above the Reply box :wink:)
gomes. said:
Im stuck in the part in bold. I can rearrange [itex]1/squareroot(x+1)=x[/itex] into [itex]x^3+x^2=1[/itex], but how do i show that x=r can solve the equation? Thanks.

there isn't really anything to prove …

"r is the root of 1/√(x+1) = x" is just another way of saying that 1/√(r+1) = r :wink:
 

What is the purpose of finding roots of an equation?

Finding roots of an equation is important in mathematics and science because it helps us solve problems and understand relationships between variables. It allows us to determine the values of variables that make the equation true.

What is a root of an equation?

A root of an equation is a value that, when substituted for the variable, makes the equation true. In other words, it is the value of the variable that satisfies the equation.

How do you find the roots of a simple linear equation?

To find the roots of a simple linear equation, set the equation equal to zero and solve for the variable. The resulting value is the root of the equation.

What is the difference between real and complex roots?

A real root is a value of the variable that is a real number, while a complex root is a value of the variable that is a complex number. In other words, a real root can be plotted on a number line, while a complex root requires a two-dimensional plane to represent.

What methods can be used to find the roots of a more complex equation?

There are several methods that can be used to find the roots of a more complex equation, such as the quadratic formula, factoring, and graphing. These methods may differ depending on the type of equation and the level of complexity.

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