Question

Fie x=√1+2+...+50/1+2+...+51 si y=√1+2+...50/1+2+...+53Calculati:a)x×y

b)x/y

Answer 1

$x= \sqrt \frac{1+2+...+50}{1+2+...+51}$
$x= \sqrt{ \frac{25*51}{51*26} }$ (asa da dupa ce faci suma gauss) => $x= \sqrt \frac{25}{26} }$
$y= \sqrt \frac{26*53}{53*27} ; y= \sqrt \frac{26}{27};$
a)$x*y= \sqrt{ \frac{25}{26}* \frac{26}{27} }; x*y= \sqrt \frac{25}{27}$; $x*y= \frac{5}{ 3\sqrt{3} }= \frac{5 \sqrt{3} }{3*3}= \frac{5 \sqrt{3} }{9}.$
b)$\frac{x}{y}= \sqrt {\frac{25}{26}* \frac{27}{26}}$