If a and b are roots of the equation $x^{2} - x + 1 = 0$ , then write the value of a² + b².

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Solution

Given: $x^{2} - x + 1 = 0$
Also, $a a n d b$ are the roots of the equation.
Then, sum of the roots = $a + b = - (\frac{- 1}{1}) = 1$

Product of the roots = $a b = \frac{1}{1} = 1$

$∴ {(a + b)}^{2} = a^{2} + b^{2} + 2 a b \Rightarrow 1^{2} = a^{2} + b^{2} + 2 \times 1 \Rightarrow a^{2} + b^{2} = 1 - 2 = - 1 \Rightarrow a^{2} + b^{2} = - 1$

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