Question

If
$\sqrt{x \div y \: + \sqrt{y \div x = 10 \div 3} }$
then find xy​

Answer 1

HEY MATE THAT IS HOW TO SOLVE IT............ ❤️❤️❤️❤️

GIVEN:

$\sqrt{ \frac{x}{y} + \sqrt{ \frac{y}{x} } } = \frac{10}{3}$

TO FIND : VALUE OF xy.

SOLUTION :

LET x/y = a, then

$\sqrt{a + \frac{1}{ \sqrt{a} } } = \frac{10}{3}$

Squaring both sides,

THIS GIVES

$a + \frac{1}{ \sqrt{a} } = \frac{100}{9}$

Again Squaring both sides,

$a {}^{2} + \frac{1}{a} + 2 \times a \times \frac{1}{ \sqrt{a} } = \frac{10000}{81}$

REPLACE.

a = x/y

YOU WILL GET THIS

$\frac{x {}^{2} }{y {}^{2} } + \frac{y}{x} + \frac{2 \sqrt{x} }{ \sqrt{y} } = \frac{10000}{81}$

NOW, FURTHER USE WOLFRAM ALPHA

IT WILL GIVE YOU SOLUTIONS.

_________THANK YOU _________