, are roots of y^2-2 y-7=0 find : α2 + β2 - Vidyadip

Question

$\alpha, \beta$ are roots of $y^2-2 y-7=0$ find : α² + β²

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Answer

$\begin{array}{l} y ^2-2 y -7=0 \\ \alpha+\beta=2 \text { and } \alpha \beta=-7 \\ \text { (1). }(\alpha+\beta)^2=\alpha^2+\beta^2+2 \alpha \beta \\ \Rightarrow(2)^2=\alpha^2+\beta^2+2(-7) \\ \Rightarrow 4+14=\alpha^2+\beta^2 \\ \Rightarrow \alpha^2+\beta^2=18\end{array}$

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