What are the solutions of the equation x4 + 3x2 + 2 = 0? use u substitution to solve. x = plus-or-minus i startroot 2 endroot and x = ±1 x = plus-or-minus i startroot 2 endroot and x = ±i x = plus-or-minus startroot 2 endroot and x = ±i x = plus-or-minus startroot 2 endroot and x = ±1

Step-by-step explanation:

We have been given an equation . We are asked to find the solutions of our given equation using u-substitution.

We can rewrite our given equation as:  

Let us assume that .

Upon substituting back the value of u, we will get:

Now we will use imaginary unit i. We know that .

Therefore, the solutions for our given equation are .

x = ± i & ± i√2

Step-by-step explanation:

The given equation is x⁴ + 3x² + 2 = 0

let u = x²

∴ u² + 3u + 2 = 0

∴ ( u + 2 ) ( u + 1 ) = 0

∴ u = -1 or -2

∴ x² = -1   or  x² = -2

∴ x = ±√(-1) = ± i

And x = ±√(-2) = ± i √2

Note i = √(-1)

step-by-step explanation: