(1-x^2+(x^4)/2)*(1-(9x^2)/2+(81x^4)/24)

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Solution for (1-x^2+(x^4)/2)*(1-(9x^2)/2+(81x^4)/24) equation: 


x in (-oo:+oo)

((x^4)/2-x^2+1)*((81*x^4)/24-((9*x^2)/2)+1) = 0

((x^4)/2-x^2+1)*((81*x^4)/24+(-9/2)*x^2+1) = 0

(1/2*x^4-x^2+1)*(27/8*x^4-9/2*x^2+1) = 0

(x^4)/2-x^2+1 = 0

1/2*x^4-x^2+1 = 0

t_1 = x^2

1/2*t_1^2-1*t_1^1+1 = 0

1/2*t_1^2-t_1+1 = 0

DELTA = (-1)^2-(1/2*1*4)

DELTA = -1

DELTA < 0

(81*x^4)/24-((9*x^2)/2)+1 = 0

(81*x^4)/24+(-9/2)*x^2+1 = 0

27/8*x^4-9/2*x^2+1 = 0

t_2 = x^2

27/8*t_2^2-9/2*t_2^1+1 = 0

27/8*t_2^2-9/2*t_2+1 = 0

DELTA = (-9/2)^2-(1*27/8*4)

DELTA = 27/4

DELTA > 0

t_2 = ((27/4)^(1/2)+9/2)/(2*27/8) or t_2 = (9/2-(27/4)^(1/2))/(2*27/8)

t_2 = 4/27*((27/4)^(1/2)+9/2) or t_2 = 4/27*(9/2-(27/4)^(1/2))

t_2 = 4/27*(9/2-(27/4)^(1/2))

x^2-(4/27*(9/2-(27/4)^(1/2))) = 0

x^2-4/27*(9/2-(27/4)^(1/2)) = 0

1*x^2 = -(-4/27*(9/2-(27/4)^(1/2))) // : 1

x^2 = 4/27*(9/2-(27/4)^(1/2))

x^2 = 4/27*(9/2-(27/4)^(1/2)) // ^ 1/2

abs(x) = (4/27)^(1/2)*(9/2-(27/4)^(1/2))^(1/2)

x = (4/27)^(1/2)*(9/2-(27/4)^(1/2))^(1/2) or x = -((4/27)^(1/2)*(9/2-(27/4)^(1/2))^(1/2))

t_2 = 4/27*((27/4)^(1/2)+9/2)

x^2-(4/27*((27/4)^(1/2)+9/2)) = 0

x^2-4/27*((27/4)^(1/2)+9/2) = 0

1*x^2 = -(-4/27*((27/4)^(1/2)+9/2)) // : 1

x^2 = 4/27*((27/4)^(1/2)+9/2)

x^2 = 4/27*((27/4)^(1/2)+9/2) // ^ 1/2

abs(x) = (4/27)^(1/2)*((27/4)^(1/2)+9/2)^(1/2)

x = (4/27)^(1/2)*((27/4)^(1/2)+9/2)^(1/2) or x = -((4/27)^(1/2)*((27/4)^(1/2)+9/2)^(1/2))

((x^4)/2-x^2+1)*((81*x^4)/24-((9*x^2)/2)+1) = 0  <=>  (x^4)/2-x^2+1 = 0 or ((x^4)/2-x^2+1)*((81*x^4)/24-((9*x^2)/2)+1) = 0  <=>  (81*x^4)/24-((9*x^2)/2)+1 = 0

x in { (4/27)^(1/2)*(9/2-(27/4)^(1/2))^(1/2), -((4/27)^(1/2)*(9/2-(27/4)^(1/2))^(1/2)), (4/27)^(1/2)*((27/4)^(1/2)+9/2)^(1/2), -((4/27)^(1/2)*((27/4)^(1/2)+9/2)^(1/2)) }

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