Let α > 0. If ∫ x/√(x+α) - √x dx = 16 + 20√2 / 15 ; x ∈ {0,α} then α is equal to :

Question

Let α > 0. If \(\int\limits_0^α \frac{x}{\sqrt{x+\alpha}-\sqrt{x}}dx=\frac{16+20\sqrt{2}}{15}\) then α is equal to

(1) 2 

(2) 4 

(3) √2 

(4) 2√2

Answer 1

Correct option is (1) 2 

After rationalising