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Summation by Sigma Method

If α, β and y...

Question

If $α, β a n d γ$ are the real roots of the equation $x^{3} + 5 x^{2} + 9 x - 6 = 0$ . Find the value of $α^{2} + β^{2} + γ^{2}$ .
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Solution

We know
${(α + β + γ)}^{2} = α^{2} + β^{2} + γ^{2} + 2 (α β + β γ + γ α)$ $α^{2} + β^{2} + γ^{2} = {(α + β + γ)}^{2} - 2 (α β + β γ + γ α)$ = ${- 5}^{2} - 2 \times 9$ = 25 - 18 = 7

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