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Question
If a and b are roots of the equation \[x^2 - x + 1 = 0\], then write the value of a2 + b2.
Solution
Given:
\[x^2 - x + 1 = 0\]
Also,
\[a \text { and } b\] are the roots of the equation.
Then, sum of the roots = \[a + b = - \left( \frac{- 1}{1} \right) = 1\]
Product of the roots = \[ab = \frac{1}{1} = 1\]
\[\therefore \left( a + b \right)^2 = a^2 + b^2 + 2ab\]
\[ \Rightarrow 1^2 = a^2 + b^2 + 2 \times 1\]
\[ \Rightarrow a^2 + b^2 = 1 - 2 = - 1\]
\[ \Rightarrow a^2 + b^2 = - 1\]
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