Given that x_(1),x_(2) are the solutions of the equation, the value of |x₁ - x₂| is 2/3√(15).
How to find the value of |x₁ - x₂|
To find the value of |x₁ - x₂|, find the solutions x₁ and x₂ of the equation

simplify the equation step by step:

Rewriting 4 and 16 as powers of 2:

Applying the power of a power rule:


Now equate the bases:

Rearranging the equation to form a quadratic equation:

Divide the equation by 2:
3x^2 - 6x - 2 = 0
Solve this quadratic equation using the quadratic formula:
x = (-b ± √(
- 4ac))/(2a),
where a = 3, b = -6, and c = -2.
Plug in the values:
x = (-(-6) ± √(
- 4 * 3 * (-2)))/(2 * 3)
x = (6 ± √(36 + 24))/(6)
x = (6 ± √(60))/(6)
x = (6 ± √(4 * 15))/(6)
x = (6 ± 2√(15))/(6)
x = 1 ± (1/3)√(15)
Therefore, the solutions to the equation are x₁ = 1 + (1/3)√(15) and x₂ = 1 - (1/3)√(15).
To find |x₁ - x₂|, substitute the values:
|x₁ - x₂| = |(1 + (1/3)√(15)) - (1 - (1/3)√(15))|
|x₁ - x₂| = |2/3√(15)|
|x₁ - x₂| = 2/3√(15)
Therefore, the value of |x₁ - x₂| is 2/3√(15).