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Squaring an Inequality

91. If alpha ...

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91. If alpha and beta are roots of equation x(square) + px - q = 0 and gama and delta are roots of equation x (square) + px + r = 0 . Then prove that the value of (alpha-gama)(alpha-delta) is (q+r).

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α

β

be the roots of

x^{2} + p x - q = 0

γ, δ

x^{2} + p x + r = 0

(α - γ) (α - δ) = (β - γ) (β - δ) = q + r

α, β

are roots of the equation

x^{2} + p x - q = 0

γ, δ

x^{2} + p x + r = 0,

then the value of

(α - γ) (α - δ)

α

β

are the roots of quadratic equation

x^{2} + p x + q = 0

γ

δ

are the roots of

x^{2} + p x - r = 0

(α - γ)

(α - δ)

α, β

are the roots of

x^{2} + p x + q = 0

γ, δ

are the roots of

x^{2} + p x + r = 0

\frac{(α - γ) (α - δ)}{(β - γ) (β - δ)} =

α, β

are the roots of

x^{2} + p x - q = 0

γ, δ

x^{2} + p x + r = 0

(α - γ) (β - γ) (α - δ) (β - δ) =

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