# Equation problem

## Homework Statement

If the equation 2x ^ 3 - 15X ^ 2 + 30 x - 7 = 0 has roots a, b ​​and c to find the value of the expression a ^ 3 + b ^ 3 + c ^ 3. Also to be found without using the types Vieta,the equation with roots 1 / (a-3), 1 / (b-3), 1 / (c-3)

## Homework Equations

I found the first part of a^3+b^3+c^3=754/8 but i cant find the second part of the exercise without using the type of vieta any ideas?

## The Attempt at a Solution

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Bacle2
Wouldn't the equation be given by:

(x-r1)(x-r2)(x-r3) ?

yea but he (x-r1)(x-r2)(x-r3) conclude to the types of vietta.. he says to find the equation without to use vietta

NascentOxygen
Staff Emeritus

## Homework Statement

If the equation 2x ^ 3 - 15X ^ 2 + 30 x - 7 = 0 has roots a, b ​​and c to find the value of the expression a ^ 3 + b ^ 3 + c ^ 3.
What method did you use to determine this?

i used the types of vietta and i found abc,a+b+c,ab+bc+ca cuz its says to not use vietta types only in second statement and then i used eulers equation

a^3+b^3+c^3=3abc+(a+b+c)(a^2+b^2+c^2-ab-bc-ca)

NascentOxygen
Staff Emeritus
i used the types of vietta and i found abc,a+b+c,ab+bc+ca cuz its says to not use vietta types only in second statement and then i used eulers equation

a^3+b^3+c^3=3abc+(a+b+c)(a^2+b^2+c^2-ab-bc-ca)
So you as good as solved for the individual roots, then multiplied all 3 to get abc, and added all 3 to get a+b+c, etc?

yea as you know vietta is formed like this

abc=-d/a, a+b+c=-b/a, ab+bc+ca=c/a

NascentOxygen
Staff Emeritus
So as you have determined 'a', can you now subtract 3 from that value of 'a' and take the reciprocal to get the new root r1, same for 'b' and 'c', and then multiply out (x-r1)(x-r2)(x-r3) ?

yea i understand but maybe this (x-r1)(x-r2)(x-r3) guide to vietta types? or not?

NascentOxygen
Staff Emeritus
Is it permissible to work it out from basics, making no reliance on Mr Vieté's formulae? 