Let alpha and beta be the roots of the equati | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\alpha$ and $\beta$ are roots of $5 x^{2}+6 x-2=0$

$\Rightarrow 5 \alpha^{2}+6 \alpha-2=0$

$\Rightarrow 5 \alpha^{n+2}+6 \alpha^{n+1}-2 \alpha^

Vedclass · Accepted Answer

$5 \mathrm{S}_{6}+6 \mathrm{S}_{5}=2 \mathrm{S}_{4}$

Vedclass · Answer

$\alpha$ and $\beta$ are roots of $5 x^{2}+6 x-2=0$

$\Rightarrow 5 \alpha^{2}+6 \alpha-2=0$

$\Rightarrow 5 \alpha^{n+2}+6 \alpha^{n+1}-2 \alpha^{n}=0 \quad \ldots(1)$

(By multiplying $\left.\alpha^{n}\right)$

Similarly $5 \beta^{n+2}+6 \beta^{n+1}-2 \beta^{n}=0 \quad \ldots(2)$

By adding (1)$\&(2)$

$5 \mathrm{S}_{\mathrm{n}+2}+6 \mathrm{S}_{\mathrm{n}+1}-2 \mathrm{S}_{\mathrm{n}}=0$

For $n=4$

$5 \mathrm{S}_{6}+6 \mathrm{S}_{5}=2 \mathrm{S}_{4}$

Let $\alpha$ and $\beta$ be the roots of the equation $5 x^{2}+6 x-2=0 .$ If $S_{n}=\alpha^{n}+\beta^{n}, n=1,2,3 \ldots$ then :

Similar Questions

If $a < 0$ then the inequality $a{x^2} - 2x + 4 > 0$ has the solution represented by

If $x$ is real, then the value of $\frac{{{x^2} + 34x - 71}}{{{x^2} + 2x - 7}}$ does not lie between

The population of cattle in a farm increases so that the difference between the population in year $n+2$ and that in year $n$ is proportional to the population in year $n+1$. If the populations in years $2010, 2011$ and $2013$ were $39,60$ and $123$,respectively, then the population in $2012$ was

Let $f(x)={{x}^{2}}-x+k-2,k\in R$ then the complete set of values of $k$ for which $y=\left| f\left( \left| x \right| \right) \right|$ is non-derivable at $5$ distinict points is

Let $\mathrm{S}$ be the set of positive integral values of $a$ for which $\frac{\mathrm{ax}^2+2(\mathrm{a}+1) \mathrm{x}+9 \mathrm{a}+4}{\mathrm{x}^2-8 \mathrm{x}+32}<0, \forall \mathrm{x} \in \mathbb{R}$. Then, the number of elements in $\mathrm{S}$ is :