Let - and - are the roots of x2-5x-7-0 and Sn-n-n- then

x^n+2+5x^n+1 7x^n=0 α^n+2+5x^n+1 7α^n=0 β^n+2+5x^n+1 7β^n=0 ⟹ #160;S_n+2+5S_n+1 7S_n=0 S_2= (α+β)^2 2αβ = 25+14=39 ⟹ S_3 + 5S_2 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Determinant

Let α and ...

Question

Let $α$ and $β$ are the roots of $x^{2} + 5 x - 7 = 0$ and $S_{n} = α^{n} + β^{n}$ , then

Open in App

Solution

Suggest Corrections

Similar questions

α, β

x^{2} - 5 x - 8 = 0

t_{n} = α^{n} - β^{n}

\frac{t_{6} - 8 t_{4}}{5 t_{5}}

α, β

x^{2} - x - 1 = 0

S_{n} = α^{n} + β^{n}

n \geq 1

n \geq 2

α

β

5 x^{2} + 6 x - 2 = 0.

S_{n} = α^{n} + β^{n}, n = 1, 2, 3, . . . . . . . . .,

α, β

x^{2} - 4 x - 3 = 0

s_{n} = α^{n} + β^{n}, n \in N

\frac{s_{7} - 4 s_{6}}{s_{5}}

α, β

375 x^{2} - 25 x - 2 = 0

S_{n} = α^{n} + β^{n}

l i m_{n \to \infty} \sum_{r = 1}^{n} S_{r}

Join BYJU'S Learning Program