Plwase solve i

Plwase solve i If XY = & x2 = y where x and y are distinct positive real numbers, then the value ofX+ 2yis (D) 12 (C) 10

Given, x^y=y^x ... (1) 

and x²=y  ... (2)

On putting the value of y in (1), we get

x^y=(x²)^x

⇒x^y= x^2x

⇒ y = 2x  [On comparing the powers of like term]

⇒ x² = 2x  [using (2)]

⇒ x² - 2x = 0

⇒ x(x - 2) = 0

⇒ x = 0 , 2

On putting the respective values of x in (2), we get

For x = 0, y = 0² = 0

and for x = 2, y = 2² = 4 

Now, the values of x, y = 0, 0 can be discarded.

So, x + 2y = 2 + 2(4) = 2 + 8 = 10