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

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Solution

The given equation is

$x^{2} - x + 1 = 0$ ...(i)

a and b are the roots of (i)

$∴$ a + b =-1 ...(ii)

and ab = 1 Now $a^{2} + b^{2} = (a + b)^{2} - 2 a b = (- 1)^{2} - 2.1 = 1 - 2 = - 1$

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