The equation x^6 + 9x^3 − 5 = 0 is of quadratic type. To solve the equation, we set W = ? The resulting quadratic equation is ?

Answer 1

x^6 +9x^3 -5 = 0

set w =x^3

resulting quadratic equation is:

w^2 +9w -5 =0

w =-9/2 +/-(1/2)sqr(81+20)

= about .525 or -9.525

w=x^3

x=cube root of w = about (.525)^1/3, (-9.525)^1/3

x = about 0.807 and -2.120

it's a 6th degree equation, which has 6 solutions, the other 4 are imaginary

x=.525^1/3. there are 3 cube roots, 2 imaginary, 1 real

x= -.5((-9+sqr1010)/2)^1/3 + .5((-9+sqr101)/2)(sqr3)i

and one more imaginary solution

then same with x=(-9.525)^1/3, 1 real, 2 imaginary solutions

Answer 2

W = x^3

The equation is W^2 +9W -5 = 0

Use quadratic formula to solve for W