Question

What is the solution set of (3x - 1)^2 = 5?


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Answer 1

The solution of the equation is
`x=(1\pm√(5))/(3)`

Explanation:

Given : Equation
`(3x-1)^2=5`

To find : What is the solution set of equation?

Solution :

Equation
`(3x-1)^2=5`

Taking root both side,

`√((3x-1)^2)=√(5)`

`3x-1=\pm√(5)`

Taking
`3x-1=√(5)`

`3x=√(5)+1`

`x=(√(5)+1)/(3)`

Taking
`3x-1=-√(5)`

`3x=-√(5)+1`

`x=(-√(5)+1)/(3)`

Therefore, the solution of the equation is
`x=(1\pm√(5))/(3)`

Answer 2

*I'll be keeping the solutions in exact form*

So firstly, square root both sides. This will split the equation into two:

`3x-1=√(5) \\ 3x-1=-√(5)`

Next, add 1 on each side:
`3x=√(5)+1 \\ 3x=-√(5)+1`

Next, divide 3 on both sides, and your answers will be
`x=(√(5)+1)/(3),(-√(5)+1)/(3)`