What are the real and complex solutions to the following equation? -2x^4+2x^2+4=0 Show all steps.

u=±1i or u=±√2

u=±2i or u=±√2

x = ± i, x = ±

Step-by-step explanation:

Given

- 2 + 2x² + 4 = 0 ( divide through by - 2 )

- x² - 2 = 0

Use the substitution x² = u , then

u² - u - 2 = 0 ← in standard form

(u - 2)(u + 1) = 0 ← in factored form

Equate each factor to zero and solve for u

u - 2 = 0 ⇒ u = 2

u + 1 = 0 ⇒ u = - 1

Change back into terms of x, that is

x² = 2 ( take the square root of both sides )

x = ±

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

x = ± = ± i

x = ± ← real solutions

x = ± i ← complex solutions

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

94

step-by-step explanation:

average the numbers and use a variable to figure out the minimum to get a 90.

(79+94+91+92+x)/5=90

x = 94