Question

a^2=5a-3,b^2=5b-3. find a/b+b/a .where a notequal b

Answer 1

Done
Hope it helps.....

Answer 2

Given
$a {}^{2} = 5a - 3 \: \: and \: \: \: b {}^{2} = 5b - 3$

$a = \sqrt{5a - 3} \: \: \: and \: \: \: b = \sqrt{5b - 3}$

Now put values into a/ b + b/a

$\sqrt{5a - 3} \div \sqrt{5b - 3} \: + \sqrt{5b - 3} \: \div \: \sqrt{5a - 3}$

Now rationalise the denominators...


root(5a-3) × root (5b-3)/root (5b-3)×root (5b-3) +
root(5b-3)×root (5a-3)/root (5a-3) × root (5a-3)

$\sqrt{(5a - 3)(5b - 3)} \div (5b - 3) \: \: + \sqrt{(5a - 3)(5b - 3)} \div \: (5a - 3)$