If α, β and γ are the roots of the equation $x^{3}$ - 3 $x^{2}$ + 5x - 9 = 0 then the value of the expression

( α + β - γ) ( β + γ -α) (γ + α - β).

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Solution

Solution: Given equation $x^{3}$ - 3 $x^{2}$ + 5x - 9 = 0

α + β + γ = 3 or ∑α = 3

αβ + βγ + γα = 5

αβγ = 9

(α + β - γ)(β + γ - α)(γ + α - β)

(∑α - 2γ)(∑α - 2α)(∑α - 2β)

(3 - 2γ)(3 - 2α)(3 - 2β)

= (9 - 6α - 6γ + 4αγ) (3 - 2β)

= (9 - 6α - 6γ + 4αγ) (3 - 2β)

=(27 - 18β - 18α +12αβ - 18γ + 12γβ + 12αγ - 8αβγ

= 27 -18×3 + 12×5 - 8×9

= 27 - 54 + 60 - 72

= -39

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If α, β and γ are the roots of the equation x3 - 3 x2 + 5x - 9 = 0 then the value of the expression ( α + β - γ) ( β + γ -α) (γ + α - β). __

If α, β and γ are the roots of the equation $x^{3}$ - 3 $x^{2}$ + 5x - 9 = 0 then the value of the expression

( α + β - γ) ( β + γ -α) (γ + α - β).

__