Question

what are the solutions of 3x^2-4=0?

Answer 1

if the equation were
3x - 4 =0
could you solve for x?

Answer 2

4/3

Answer 3

you do the same thing, except you get

x^2 = 4/3

Answer 4

now take the square root of both sides

Answer 5

is it x=2√3

Answer 6

you start with 4/3
so you get ±sqrt(4/3) or ±2/sqrt(3) (divide by sqrt(3) )

however, people don't like sqrt in the denominator, so they multiply top and bottom by sqrt of 3 like this
\[ \frac{2}{\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}= \frac{2\sqrt{3}}{3}\]
and it is plus or minus (both will work in the equation)
\[ ± \frac{2\sqrt{3}}{3}\]

Answer 7

oh ok i see

Answer 8

in case it is not obvious
\[ \sqrt{\frac{4}{3}} \text{ can be written as }\frac{\sqrt{4}}{\sqrt{3}}= \frac{2}{\sqrt{3}}\]

Answer 9

ok. thanks a lot for your help (: