If a² + b² = 144, a × b = 24 and a > b, then find the value of $$\frac{a - b}{a + b}$$.​​

Correct option is B

Given: ​

a² +b² = 144,  a × b = 24 , and a > b

Formula Used: ​

​$$(a+b)^2 = a^2+b^2+2ab \\ \ \\ (a-b)^2 = a^2+b^2-2ab$$ 

Solution: ​

(a + b)² = 144 + 2×24 = 192  

a + b = $$\sqrt{192}$$​​

(a - b)² = 144 - 2×24 = 96 

a - b = $$\sqrt{96}$$ 

Now, 

​$$\frac{a-b}{a+b} = \frac{\sqrt{96}}{\sqrt{192}} = \sqrt{\frac{96}{192}} =\sqrt{\frac12}$$​​