Question

√p/q+√q/p=10/3 find the value of p:q

Answer 1

Answer:

p/q = 9

Step-by-step explanation:

√p/q+√q/p=10/3

put $\sqrt{\frac{p}{q} } = x$

therefore  $\sqrt{\frac{q}{p} } = \frac{1}{x}$

$\sqrt{x} +\sqrt{\frac{1}{x} }$= 10/3

squaring both the side we get

x+1/x =100/9-2

x+1/x= 82/9

9x^2-82x+9=0

solving this quadratic equation we get

x= 9 and x= 1/9

therefore,comparing we get,  p/q = 9

Answer 2

Answer:

1/9  or  9

Step-by-step explanation:

√p/q+√q/p=10/3

Squaring both sides

p/q  + q/p  + 2 * √p/q * √q/p = 100/9

=> p/q  + q/p +  2 = 100/9

=>  p/q  + q/p = 82/9

=> p² + q²  = 82pq/9

=> 9p² + 9q² = 82pq

=> 9p² - 82pq + 9q² = 0

=> 9p² - 81pq - pq + 9q² = 0

=> 9p(p - 9q) - q(p - 9q) = 0

=> (9p - q)(p - 9q) = 0

=> 9p - q = 0 => p/q = 1/9

p - 9q => p/q = 9

the value of p:q   1/9  or  9