- #1
Yes, that is correct. You could make it look nicer by "rationalizing the denominator": multiply both numerator and denominator by [itex]\sqrt{5}- 3[/itex] and you getscientist said:Is this correct?
3x + x*sqrt(5) = 2
solution
(3x + x*sqrt(5)) = 2
I factored out the x
x (3 + sqrt(5)) = 2
Divide both sides by sqrt(5) + 3
x (3 + sqrt(5) / (sqrt(5) + 3) = (2) / (sqrt(5) + 3)
cancel
x = (2) / (sqrt(5) + 3) final answer
Is this correct?
A radical equation is an equation that contains a variable inside a radical, such as a square root or cube root.
To solve a radical equation, isolate the radical on one side of the equation and then raise both sides to the appropriate power to eliminate the radical. Repeat this process until the variable is isolated and the equation is simplified.
Some common mistakes when solving radical equations include forgetting to eliminate the radical by raising both sides to the appropriate power, forgetting to check for extraneous solutions, and making errors when simplifying the equation.
To check for extraneous solutions, substitute the solution back into the original equation and see if it makes the equation true. If it does not, then it is an extraneous solution and should be discarded.
No, not all radical equations have real number solutions. Some equations may have complex solutions or no solution at all. It is important to check for extraneous solutions and domain restrictions when solving radical equations.