Let α,β(α>β) be the roots of the quadratic equation x2−x−4=0. If Pn=αn−βn,n∈N then P15P16−P14P16−P152+P14P15P13P14 is equal to

Pn−Pn−1=αn−βn−(αn−1−βn−1)=αn−2(α2−α)−βn−2(β2−β) =4(αn−2−βn−2)=4Pn−2 (P15−P14)(P16−P15)P13P14=16

Let α,β(α>β) be the roots of the quadratic equation x2−x−4=0. If Pn=αn−βn,n∈N then P15P16−P14P16−P152+P14P15P13P14 is equal to

Pn−Pn−1=αn−βn−(αn−1−βn−1)=αn−2(α2−α)−βn−2(β2−β) =4(αn−2−βn−2)=4Pn−2 (P15−P14)(P16−P15)P13P14=16

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Let $α, β (α > β)$ be the roots of the quadratic equation $x^{2} - x - 4 = 0$ . If $P_{n} = α^{n} - β^{n}, n \in N$ then $\frac{P_{15} P_{16} - P_{14} P_{16} - P_{15}^{2} + P_{14} P_{15}}{P_{13} P_{14}}$ is equal to

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$P_{n} - P_{n - 1} = α^{n} - β^{n} - (α^{n - 1} - β^{n - 1}) = α^{n - 2} (α^{2} - α) - β^{n - 2} (β^{2} - β) = 4 (α^{n - 2} - β^{n - 2}) = 4 P_{n - 2} \frac{(P_{15} - P_{14}) (P_{16} - P_{15})}{P_{13} P_{14}} = 16$

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Let α,β(α>β) be the roots of the quadratic equation x2−x−4=0. If Pn=αn−βn,n∈N then P15P16−P14P16−P152+P14P15P13P14 is equal to

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Let $α, β (α > β)$ be the roots of the quadratic equation $x^{2} - x - 4 = 0$ . If $P_{n} = α^{n} - β^{n}, n \in N$ then $\frac{P_{15} P_{16} - P_{14} P_{16} - P_{15}^{2} + P_{14} P_{15}}{P_{13} P_{14}}$ is equal to