Найдите сумму всех корней уравнения 5x^4-8x^2+1=0

5x^4-8x^2+1=0

x^2 = t; t>0

5t^2 - 8t + 1 = 0

D = (-8) ^2 - 4*5*1 = 44

√D = - / + 2 √11

t = 1/10 * (8 - / + 2√11)

t1 = (8 - 2√11) / 10 = (4-√11) / 5; x^2 = (4-√11) / 5

x1 = - √ (4-√11) / 5

x2 = √ (4-√11) / 5

t2 = (8 + 2√11) / 10 = (4+√11) / 5; x^2 = (4+√11) / 5

x3 = - √ (4+√11) / 5

x4 = √ (4+√11) / 5

сумма всех корней (x1+x2) + (x3+x4) = 0+0 = 0