Question

2+28=30+100=130=160+2000=​

Answer 1

Step-by-step explanation:

The following method can solve for ak+bk+ck .

ab+bc+ca=(a+b+c)2−(a2+b2+c2)2

ab+bc+ca=16–62

ab+bc+ca=5

abc=(a3+b3+c3)−(a+b+c)(a2+b2+c2−(ab+bc+ca))3

abc=43

Construct an equation with a,b,c as roots

x3−(a+b+c)x2+(ab+bc+ca)x−abc=0

x3−4x2+5x−43=0

3x3−12x2+15x−4=0

Using this construct an equation with a4,b4,c4 as roots.

This can be done by replace x with x14 and convert it into a cubic equation

Let y=x14

3y3−12y2+15y−4=0

3y3+15y=12y2+4

squaring on both sides

9y6+90y4+225y2=144y4+96y2+16

9y6+129y2=54y4+16

squaring on both sides

81y12+2322y8+16641y4=2916y8+1728y4+256

replace y4 with x

81x3+2322x2+16641x=2916x2+1728x+256

81x3−594x2+14913x−256=0

Now sum of roots = 59481

Answer 2

2+28=30+100=130

160 + 2000 = 2160