Question

determine the root of the following equation
√3n -5+7 = 2√3n-5+5

Answer 1

To determine the root of the equation, we need to isolate the variable on one side of the equation. Let's begin by simplifying the equation:

√3n - 5 + 7 = 2√3n - 5 + 5

Combining like terms:

√3n + 2 = 2√3n

Next, let's eliminate the square root by squaring both sides of the equation:

(√3n + 2)^2 = (2√3n)^2

Expanding both sides:

(3n + 4√3n + 4) = (4 * 3n)

Simplifying the right side:

3n + 4√3n + 4 = 12n

Now, let's isolate the terms with the variable on one side:

3n - 12n = -4 - 4√3n

-9n = -4(1 + √3n)

Dividing both sides by -9:

n = (4/9)(1 + √3n)

At this point, we have isolated the variable n. However, we cannot determine a specific numerical value for n without knowing the value of √3n.

Answer 2

starting from this step:
√3n + 2 = 2√3n
2 = 2√3n
1 = √3n
1 = 3n
n = 1/3

Answer 3

Apologies for the mistake. Let's correct the solution:

Starting from the step:
√3n + 2 = 2√3n

We can subtract √3n from both sides:

2 = √3n

Now, we can square both sides of the equation to eliminate the square root:

(2)^2 = (√3n)^2

4 = 3n

Finally, we can divide both sides by 3 to solve for n:

4/3 = n

Therefore, the root of the equation is n = 4/3.