If alpha and beta are the roots of the quad | vedclass

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

Question

$x^{2}+x \sin 	heta-2 \sin 	heta=0$

$\alpha+\beta=-\sin 	heta$

$\alpha \beta=-2 \sin 	heta$

$	ext { Now, } \frac{\alpha^{12}+\beta^{12}}

Vedclass · Accepted Answer

$\frac{{{2^{12}}}}{{{{\left( {\sin \,	heta  + 8} ight)}^{12}}}}$

Vedclass · Answer

$x^{2}+x \sin 	heta-2 \sin 	heta=0$

$\alpha+\beta=-\sin 	heta$

$\alpha \beta=-2 \sin 	heta$

$	ext { Now, } \frac{\alpha^{12}+\beta^{12}}{\left(\frac{1}{\alpha^{12}}+\frac{1}{\beta^{12}}ight)(\alpha-\beta)^{24}}$

$=\frac{(\alpha \beta)^{12}}{(\alpha-\beta)^{24}}$

$=\frac{(\alpha \beta)^{12}}{\left((\alpha+\beta)^{2}-4 \alpha \betaight)^{12}}$

$=\left[\frac{\alpha \beta}{(\alpha+\beta)^{2}-4 \alpha \beta}ight]^{12}$

$=\left(\frac{-2 \sin 	heta}{\sin ^{2} 	heta+8 \sin 	heta}ight)^{12}$

$=\frac{2^{12}}{(\sin 	heta+8)^{12}}$

Similar Questions

The real roots of the equation ${x^2} + 5|x| + \,\,4 = 0$ are

Let $x$ and $y$ be two $2-$digit numbers such that $y$ is obtained by reversing the digits of $x$. Suppose they also satisfy $x^2-y^2=m^2$ for some positive integer $m$. The value of $x+y+m$ is

If the sum of the two roots of the equation $4{x^3} + 16{x^2} - 9x - 36 = 0$ is zero, then the roots are

If $\alpha ,\beta ,\gamma $are the roots of the equation ${x^3} + x + 1 = 0$, then the value of ${\alpha ^3}{\beta ^3}{\gamma ^3}$

The number of real roots of the polynomial equation $x^4-x^2+2 x-1=0$ is