What are the solutions of the equation x^4 + 6x^2 + 5 = 0? Use u substitution to solve.

second option

Step-by-step explanation:

Given

+ 6x² + 5 = 0

let u = x², then

u² + 6u + 5 = 0 ← in standard form

(u + 1)(u + 5) = 0 ← in factored form

Equate each factor to zero and solve for u

u + 1 = 0 ⇒ u = - 1

u + 5 = 0 ⇒ u = - 5

Change u back into terms of x, that is

x² = - 1 ( take the square root of both sides )

x = ± = ± i ( noting that = i ), and

x² = - 5 ( take the square root of both sides )

x = ± = ± = ± × = ± i

Solutions are x = ± i and x = ± i

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you