Дано

x1+x2=7

x1*x2=2

Найти

x1^4-x2^4 (^4 - степень)

X1+x2=7, x1*x2=2

x1=7-x2

x2 * (7-x2) = 2

x2²-7x2+2=0

D=49-8=41

1) x2 = (7-√41) / 2⇒x1=7 - (7-√41) / 2 = (7+√41) / 2

2) x2 = (7+√41) / 2⇒x1 = (4-√41) / 2

x1^4-x2^4 = (x1²-x2²) (x1²+x2²) = (x1+x2) (x1-x2) * [ (x1+x2) ²-2x1*x2]=

=7 * (49-4) (х1-х2) = 315 * (х1-х2)

1) 315*[ (7+√41) / 2 - (7-√41) / 2]=315*√41

2) 315*[ (7-√41) / 2 - (7+√41) / 2]=-315√41