2x2−6x+5=0 ⟹ a=2,b=−6,c=52x^{2} - 6x + 5 = 0 \implies a = 2, b = -6, c = 52x2−6x+5=0⟹a=2,b=−6,c=5
α+β= −ba= −(−6)2=3\alpha + \beta = \; \frac{-b}{a} = \; \frac{-(-6)}{2} = 3α+β=a−b=2−(−6)=3
αβ= ca= 52\alpha\beta = \; \frac{c}{a} = \; \frac{5}{2}αβ=ac=25
βα+ αβ= β2 + α2αβ\; \frac{\beta}{\alpha} + \; \frac{\alpha}{\beta} = \; \frac{\beta^{2}\;+\;\alpha^{2}}{\alpha\beta}αβ+βα=αββ2+α2
(α + β)2 − 2αβαβ= 32 − 2(52)52\; \frac{(\alpha\;+\;\beta)^{2}\; -\;2\alpha\beta}{\alpha\beta} = \; \frac{3^{2}\; -\;2\left(\frac{5}{2}\right)}{\frac{5}{2}}αβ(α+β)2−2αβ=2532−2(25)
= 452= 85\; \frac{4}{\frac{5}{2}} = \; \frac{8}{5}254=58