Verified answer

2x²+7x+1=0

D= 49-8=41

x1= (-7+√41)/4

x2= (-7-√41)/4

а) x1³+3x1²*x2+3x1*x2²+x2³= (x1+x2)³

((-7+√41-7-√41)/4)³= (-14/4)³= (-7/2)³= -343/8= -42,875

б) x1³/x2 + x2³/x1= (x1^4+x2^4)/x1x2

(-7+√41)²*(-7+√41)²/256= (16136-2520√41)/256= (2017-315√41)/32

(-7-√41)²*(-7-√41)²/256= (16136+2520√41)/256= (2017+315√41)/32

(2017-315√41+2017+315√41)/32= 4034/32=2017/16

(-7+√41)*(-7-√41)/16= (49+7√41-7√41-41)/16= 8/16= 1/2

2017/16:1/2= 2017/16*2= 2017/8= 252,125