Solve:

Question

(x^4)+(x^2)+1=0?

Answer 1

The equation is (x⁴) + (x²) + 1 = 0

x⁴ + x² + x² - x²+ 1 = 0

(x⁴ + 2 x² + 1) - x² = 0

(x² + 1)² - x² = 0

Therefore   a² - b² = (a + b) (a - b)

(x² +  x + 1) (x² -  x + 1) = 0

x² +  x + 1 = 0                              (or)      x²-  x + 1 = 0

Therefore           x = {-b ± √[b² - 4(a)(c)]} /2(a)

x =  {-1 ± √[ 1-4(1)(1) ] }/ 2(1)         (or)   x =  {1 ± √[ 1 - 4(1)(1) ]} / 2(1)

x =  }-1 ± √[ -3 ]} / 2                        (or)  x = { 1 ± √[ -3 ] }/ 2

x =  -1 ± √3i / 2                              (or)  x =  1 ± √3i / 2

x = -1 + √3i / 2 , -1 - √3i / 2           (or)  x =  1 + √3i / 2 , 1 - √3i / 2

The solution are  x = -1 + √3i / 2 , -1 - √3i / 2  and  x =  1 + √3i / 2 , 1 - √3i / 2.