Question

If a,b are the roots of x^2-3x+1=0, find the equation whose roots are 1+a+a^2 & 1+b+b^2
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ANSWER=x^2-12x+16=0

Answer 1

sum = 3
product = 1

Answer 2

sum of roots = a^2+a+1+1+b+b^2

Answer 3

so you know a+b=3
ab=1

Answer 4

hmm :)

Answer 5

you just need a^2 6b^2, right ?

Answer 6

a^2+b^2

Answer 7

how to sum those

Answer 8

a^2+b^2 = (a+b)^2 -2ab
i think we did this last time ?

Answer 9

yes

Answer 10

2+(a+b)^2-2ab+(a+b)

Answer 11

okk...for this, so now you have sum, just need product, ...
(a^2+a+1)(1+b+b^2 )

Answer 12

is this right?

Answer 13

yes, just plug in values.

Answer 14

ok

Answer 15

12

Answer 16

yes.

Answer 17

now product

Answer 18

1+b+b^2+a+ab+ab^2+a^2+a^2b+a^2b^2

Answer 19

is this right?

Answer 20

yes.

Answer 21

whats next?

Answer 22

1+b+b^2+a+ab+ab^2+a^2+a^2b+a^2b^2
= 1+ (a+b) + ab + (a^2+b^2) + (ab)^2 + ab (a+b)

Answer 23

this is just like my anime....

Answer 24

which term you have doubt ?

Answer 25

which anime?

Answer 26

16

Answer 27

yeah, so u got the equation ?