Question

$\sf{lt \: is \: known \: that \: x = 9 \: is \: root \: of \: the \: equation}$ $\sf{ log_{\pi}( {x}^{2} + 15 {a}^{2} ) - log_{\pi}(a - 2) = log_{\pi} \frac{8ax}{a - 2}}$ $\sf{find \: the \: other \: roots \: of \: this \: equation}$ ​

Answer 1

Step-by-step explanation:

log a-logb = log(a/b)

so

$log_{\pi}( {x}^{2} + 15 {a}^{2} ) - log_{\pi}(a - 2) = log_{\pi}( \frac{8ax}{a - 2} )$

$log_{\pi}( \frac{ {x}^{2} + 15 {a}^{2} }{a - 2} ) = log_{\pi}( \frac{8ax}{a - 2} )$

remove log on both sides

(x^2+15a^2)/(a-2)= 8ax/(a-2)

(x^2+15a^2)=8ax

so 9 is the one of the roots

so

81+15a^2=8*9a

15a^2-72a+81=0

5a^2-24a+27=0

5a^2-15a-9a+27=0

5a(a-3)-9(a-3)=0

(a-3)(5a-9)=0

a=3 or 5a=9

a=9/5

put these values in the above equation and find other root

if we take 9/5 we will get negative in the place of a-2 so

a=3

so equation will be x^2+15*9=8*3*x

x^2-24x+135=0

so sum of the zeros =(-b/a)= 24

9+β=24

β=24-9

β=15

Answer 2

Answer:

Let X,Y and Z be three jointly continuous random variables with joint PDF

fXYZ(x,y,z)=⎧⎩⎨⎪⎪13(x+2y+3z)00≤x,y,z≤1otherwise

Find the joint PDF of X and Y, fXY(x,y)