Question

How do you solve `(x-2/3)^2 - 8= 1/3`?

Answer 1

`x_1=(2-5sqrt3)/3` and `x_2=(2+5sqrt3)/3`

Explanation:

`(x-2/3)^2-8=1/3`

`(x-2/3)^2-25/3=0`

`(x-2/3)^2-75/9=0`

`(x-2/3)^2-((5sqrt3)/3)^2=0`

`(x-2/3+(5sqrt3)/3)*(x-2/3-(5sqrt3)/3)=0`

Hence `x_1=(2-5sqrt3)/3` and `x_2=(2+5sqrt3)/3`