Question

What is the solution set of the equation x+3x+2=3+1x? Note: x≠0, −2 {−1, 1} {2} {−1, 2} {−1}

Answer 1

Answer:

Interpreting as: x+3x+2=3+1x

Input:

x + 3 x + 2 = 3 + 1 x

Result:

4 x + 2 = x + 3

Answer 2

We want to find the solution set of the equation:

x + 3x + 2 = 3 + 1/x

The solution set is { (1 + √17)/8, (1 - √17)/8)}

To find this, we just need to solve the equation for x.

We start with:

x + 3x + 2 = 3 + 1/x

We simplify this to:

(x + 3x) + 2 = 3 + 1/x

4x + 2 = 3 + 1/x

4x + 2 - 3 - 1/x = 0

4x - 1 - 1/x = 0

Then we multiply by x in both sides to get:

4x^2 - x - 1 = 0

This is just a quadratic equation, the solutions are given by Bhaskara's equation.

$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*4*(-1)} }{2*4} \\\\x = \frac{1 \pm \sqrt{17} }{8}$

Then the solution set is: { (1 + √17)/8, (1 - √17)/8)}

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