Radical Equation question?????

Question

Solve the problem, and check for extraneous solutions:

1. 4x - (x * 3^(1/2)) = 6

Sorry, it's very hard to do square roots. It should just be x root 3 if u know what i mean. neway, thanks so much for your help!!!

Answer 1

4x - √3 x = 6

(4 - √3) x = 6

x = 6 / (4 - √3)

x = 6 (4 + √3)  /  (4 - √3)(4 + √3)

x = 6 (4 + √3)  /  13

x = (6 / 13) (4 + √3)

Answer 2

Do you mean 4X- (3X)^1/2=6?

Answer 3

4x - x√3 = 6

factor the x from the two terms on the left side

x(4-√3) = 6

divide by the complex number

x = 6/ (4-√3)

at this point you can put it into a scientific calculator

x = 2.65

or if you are suppose to leave it in radical form then you should rationalize the denominator by multiplying by the complex conjugate (4+√3).

x = 6 (4 + √3) / (4 - √3)(4 + √3)

x = 6 (4 + √3) / (4*4 - √3 * √3 )

x = 6 (4 + √3) / 13

x = (6 / 13) (4 + √3)

Answer 4

Then,x^3/2=4x-6,x^3=16x^2-48x^2=36,then x^3+48x^2-16x^2-36=0,Then look for x,it must have atleast one real solution.