Question 767458
Q:
The equation {{{x^2-2x-11=0}}} has solutions a and b. Find the value of {{{a^2 + b^2}}}.
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The sum of the roots of a quadratic equation {{{Ax^2 + Bx + C = 0}}} is equal to {{{(-B)/A}}} and the product of the roots is equal to {{{C/A}}}.
In {{{x^2-2x-11=0}}}, a + b = {{{(-(-2))/1}}} = 2 and ab = {{{(-11)/1}}} = -11.
{{{(a + b)^2}}} = {{{a^2 + 2ab + b^2}}}
so {{{a^2 + b^2}}} = {{{(a+b)^2 - 2ab}}} = {{{2^2 - 2(-11)}}} = {{{highlight(26)}}}.
ANSWER: {{{highlight(26)}}}