Question 1011284
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If r and s are the roots of x^2 -8x +6 =0, find r^2 + 3rs +s^2.
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You do not need to solve the equation and manipulate with the roots to answer the question.

If r and s are the roots of the equation {{{x^2 -8x +6}}} = {{{0}}}, then

r + s = 8,
rs = 6.         *) see an explanation below, after the problem' solution.

Then {{{(r + s)^2}}} = {{{r^2 + 2rs + s^2}}} = 64.

Add rs = 6 to both sides, and you will get 

{{{r^2 + 3rs +s^2}}} = 64 + 6 = 70.

<U>Answer</U>. {{{r^2 + 3rs +s^2}}} = 70.
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*) If r and s are the roots of the equation {{{x^2 + px +q}}} = {{{0}}}, then the factorization takes place {{{x^2 + px +q}}} = (x-r)*(x-s).

If you open parentheses, you will get   r + s = -p   and  rs = q.

The problem in the claim is aimed to teach the student these identities and to teach him/her to apply them.
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