Question

It alpha and beta are zeros of x² - 4x +3. Then find the
values of
1/alpha^2+1/beta^2​

Answer 1

${x}^{2} - 4x + 3 = 0 \\ \\ {x}^{2} - 3x - x + 3= 0 \\ \\ x(x - 3) - 1(x - 3) \\ \\ (x - 3)(x - 1) \\ \\ x = 3 \: or \: x = 1 \\ \\ \alpha = 3 \: and \: \beta = 1 \\ \\ \frac{1}{ \alpha ^{2} } + \frac{1}{ \beta ^{2} } = \frac{ \alpha ^{2} + \beta ^{2} }{ { \alpha }^{2} { \beta }^{2} } \\ \\ = \frac{ {3}^{2} + {1}^{2} }{ {3}^{2} \times {1}^{2} } = \frac{9 + 1}{9} \\ \\ = \frac{10}{9} </p><p>$

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