Question

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


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Answer 1

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

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

$3x-1=\sqrt{5} \\ 3x-1=-\sqrt{5}$

Next, add 1 on each side: $3x=\sqrt{5}+1 \\ 3x=-\sqrt{5}+1$

Next, divide 3 on both sides, and your answers will be $x=\frac{\sqrt{5}+1}{3},\frac{-\sqrt{5}+1}{3}$

Answer 2

Answer:

The solution of the equation is $x=\frac{1\pm\sqrt{5}}{3}$

Step-by-step 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,

$\sqrt{(3x-1)^2}=\sqrt{5}$

$3x-1=\pm\sqrt{5}$

Taking $3x-1=\sqrt{5}$

$3x=\sqrt{5}+1$

$x=\frac{\sqrt{5}+1}{3}$

Taking $3x-1=-\sqrt{5}$

$3x=-\sqrt{5}+1$

$x=\frac{-\sqrt{5}+1}{3}$

Therefore, the solution of the equation is $x=\frac{1\pm\sqrt{5}}{3}$