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Roots of a Quadratic Equation

If α, β are t...

Question

If $α, β$ are the roots of the equation $x^{2} - 4 x + 3 = 0,$ then the value of $\sqrt{α^{4} + β^{4} - 1}$ is

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Solution

$x^{2} - 4 x + 3 = 0$
$\Rightarrow x^{2} - x - 3 x + 3 = 0$
$\Rightarrow (x - 1) (x - 3) = 0$
$\Rightarrow x = 1, 3$
Now,
$\sqrt{α^{4} + β^{4} - 1} = \sqrt{1^{4} + 3^{4} - 1} = 3^{2} = 9$

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