If  $$a^2+b^2 = 90$$​ and ab = 27, then find the possible value of $$\frac{a+b}{a-b}.$$​​

Correct option is A

Given:
  $$a^2+b^2 = 90$$ and ab = 27
Formula Used:
​$$(a-b)^2 = a^2+ b^2- 2ab \\ (a+ b)^2 = a^2+ b^2+ 2ab\\$$ 
Solution:
​$$(a + b)^2 = a^2 + b^2 + 2ab \\(a + b)^2 = 90 + 2 × 27 \\(a + b)^2 = 90 + 54 = 144 \\So, (a + b) = \sqrt{144} = 12 \\(a - b)^2 = a^2 + b^2 - 2ab \\(a - b)^2 = 90 - 2 × 27 \\(a - b)^2 = 90 - 54 = 36 \\So, (a - b) = \sqrt{36} = 6 \\(a + b) = 12 \text{and} (a - b) = 6 \\$$​​
The possible value of $$\frac{a + b}{a - b} = \frac{12}6=2$$​​